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Articles de revues sur le sujet « Scaling asymptotics »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 31 juillet 2025

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1

Paoletti, Roberto. "Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization." International Journal of Mathematics 25, no. 06 (2014): 1450060. http://dx.doi.org/10.1142/s0129167x14500608.

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This paper deals with the local semiclassical asymptotics of a quantum evolution operator in the Berezin–Toeplitz scheme, when both time and phase space variables are subject to appropriate scalings in the neighborhood of the graph of the underlying classical dynamics. Global consequences are then drawn regarding the scaling asymptotics of the trace of the quantum evolution as a function of time.

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PAOLETTI, ROBERTO. "SCALING ASYMPTOTICS FOR QUANTIZED HAMILTONIAN FLOWS." International Journal of Mathematics 23, no. 10 (2012): 1250102. http://dx.doi.org/10.1142/s0129167x12501029.

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In recent years, the near diagonal asymptotics of the equivariant components of the Szegö kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.

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3

Riley, N. "Scaling, self-similarity, and intermediate asymptotics." European Journal of Mechanics - B/Fluids 17, no. 3 (1998): 389–90. http://dx.doi.org/10.1016/s0997-7546(98)80266-5.

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Hashorva, Enkelejd, and Anthony G. Pakes. "Tail asymptotics under beta random scaling." Journal of Mathematical Analysis and Applications 372, no. 2 (2010): 496–514. http://dx.doi.org/10.1016/j.jmaa.2010.07.045.

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VENEZIANO, DANIELE. "LARGE DEVIATIONS OF MULTIFRACTAL MEASURES." Fractals 10, no. 01 (2002): 117–29. http://dx.doi.org/10.1142/s0218348x02000872.

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We analyze the extremes of stationary multifractal measures using large deviation theory. We consider various cases involving discrete multiplicative cascades: scalar or vector cascades with dependent or independent generators, bare or dressed measures, and marginal (single-point) or joint (multi-point) extremes. In each case, we obtain the scaling behavior of the probability of large deviations as the resolution of the cascade diverges. Existing rough exponential limits for scalar cascades are confirmed, whereas for other cases our scaling relationships differ from previously published result

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Xiao, Lechao, Hong Hu, Theodor Misiakiewicz, Yue M. Lu, and Jeffrey Pennington. "Precise learning curves and higher-order scaling limits for dot-product kernel regression ^*." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 11 (2023): 114005. http://dx.doi.org/10.1088/1742-5468/ad01b7.

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Abstract As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes. Currently, theoretical understanding of the learning curves (LCs) that characterize how the prediction error depends on the number of samples is restricted to either large-sample asymptotics ( m → ∞ ) or, for certain simple data distributions, to the high-dimensional asymptotics in which the number of samples scales linearly with the dimension ( m ∝ d ).

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Szpak, Nikodem. "Asymptotics from Scaling for Nonlinear Wave Equations." Communications in Partial Differential Equations 35, no. 10 (2010): 1876–90. http://dx.doi.org/10.1080/03605300903540935.

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PAOLETTI, ROBERTO. "LOCAL TRACE FORMULAE AND SCALING ASYMPTOTICS IN TOEPLITZ QUANTIZATION." International Journal of Geometric Methods in Modern Physics 07, no. 03 (2010): 379–403. http://dx.doi.org/10.1142/s021988781000435x.

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A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here, we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szegö kernel along the diagonal.

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9

Shiffman, Bernard, Steve Zelditch, and Qi Zhong. "Random zeros on complex manifolds: conditional expectations." Journal of the Institute of Mathematics of Jussieu 10, no. 3 (2011): 753–83. http://dx.doi.org/10.1017/s1474748011000041.

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AbstractWe study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The conditional distribution is analogous to the pair correlation function of zeros but we show that it has quite a different small distance behaviour. In particular, the conditional distribution does not exhibit repulsion of zeros in dimension 1. To prove this, we give universal scaling asymptotics for around p. The key tool is the conditional Szegő kernel and

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Ignat, Tatiana I. "Asymptotics for nonlocal evolution problems by scaling arguments." Differential Equations & Applications, no. 4 (2013): 613–26. http://dx.doi.org/10.7153/dea-05-36.

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Calka, Pierre, and J. E. Yukich. "Variance asymptotics and scaling limits for Gaussian polytopes." Probability Theory and Related Fields 163, no. 1-2 (2014): 259–301. http://dx.doi.org/10.1007/s00440-014-0592-6.

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Calka, Pierre, and J. E. Yukich. "Variance asymptotics and scaling limits for random polytopes." Advances in Mathematics 304 (January 2017): 1–55. http://dx.doi.org/10.1016/j.aim.2016.08.006.

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Shen, Jianhong, and Gilbert Strang. "Asymptotics of Daubechies Filters, Scaling Functions, and Wavelets." Applied and Computational Harmonic Analysis 5, no. 3 (1998): 312–31. http://dx.doi.org/10.1006/acha.1997.0234.

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14

Fel, Leonid G. "Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization." Mathematics 13, no. 2 (2025): 281. https://doi.org/10.3390/math13020281.

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We consider a wide class of summatory functions Ff;N,pm=∑k≤Nfpmk, m∈Z+∪{0} associated with the multiplicative arithmetic functions f of a scaled variable k∈Z+, where p is a prime number. Assuming an asymptotic behavior of the summatory function, F{f;N,1}=N→∞G1(N)1+OG2(N), where G1(N)=Na1logNb1, G2(N)=N−a2logN−b2 and a1,a2≥0, −∞<b1,b2<∞, we calculate the renormalization function Rf;N,pm, defined as a ratio Ff;N,pm/F{f;N,1}, and find its asymptotics R∞f;pm when N→∞. We prove that a renormalization function is multiplicative, i.e., R∞f;∏i=1npimi=∏i=1nR∞f;pimi with n distinct primes pi. We e

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15

Iksanov, Alexander, Alexander Marynych, and Matthias Meiners. "Asymptotics of random processes with immigration I: Scaling limits." Bernoulli 23, no. 2 (2017): 1233–78. http://dx.doi.org/10.3150/15-bej776.

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Barenblatt, G. I., and A. J. Chorin. "New Perspectives in Turbulence: Scaling Laws, Asymptotics, and Intermittency." SIAM Review 40, no. 2 (1998): 265–91. http://dx.doi.org/10.1137/s0036144597320047.

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Paoletti, Roberto. "Equivariant local scaling asymptotics for smoothed Töplitz spectral projectors." Journal of Functional Analysis 269, no. 7 (2015): 2254–301. http://dx.doi.org/10.1016/j.jfa.2015.03.007.

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18

Camosso, Simone. "Scaling asymptotics of Szegö kernels under commuting Hamiltonian actions." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 6 (2016): 2027–59. http://dx.doi.org/10.1007/s10231-016-0552-0.

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19

NICODEMUS, ROLF, S. GROSSMANN, and M. HOLTHAUS. "The background flow method. Part 2. Asymptotic theory of dissipation bounds." Journal of Fluid Mechanics 363 (May 25, 1998): 301–23. http://dx.doi.org/10.1017/s0022112098001177.

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We study analytically the asymptotics of the upper bound on energy dissipation for the two-dimensional plane Couette flow considered numerically in Part 1 of this work, in order to identify the mechanisms underlying the variational approach. With the help of shape functions that specify the variational profiles either in the interior or in the boundary layers, it becomes possible to quantitatively explain all numerically observed features, from the occurrence of two branches of minimizing wavenumbers to the asymptotic parameter scaling with the Reynolds number. In addition, we derive a new var

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20

HONDA, K. "SCALING THEORY ON GROWING ROUGH SURFACES." Fractals 04, no. 03 (1996): 331–37. http://dx.doi.org/10.1142/s0218348x96000443.

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We study the dynamics of growth processes of rough surfaces based on mathematical models such as the Kardar-Parisi-Zhang equation. The white-noise assumption in the KPZ equation is, however, noted to fail for higher dimensional cases. A careful continuum limit leads to a smooth surface solution for the cases. We develop the scaling theory to give an insight into the problem, by means of the intermediate asymptotics of the second kind, which is a very useful notion for the purpose. We find the roughness exponent and the dynamic exponent as functions of the substrate dimensionality for a model e

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21

Odnobokov, N. Yu. "Asymptotics of stationary measure under scaling in stochastic exchange processes." Moscow University Mathematics Bulletin 68, no. 1 (2013): 32–36. http://dx.doi.org/10.3103/s0027132213010063.

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Paoletti, Roberto. "A note on scaling asymptotics for Bohr-Sommerfeld Lagrangian submanifolds." Proceedings of the American Mathematical Society 136, no. 11 (2008): 4011–17. http://dx.doi.org/10.1090/s0002-9939-08-09410-0.

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23

L'vov, Victor S., and Itamar Procaccia. "“Intermittency” in Hydrodynamic Turbulence as Intermediate Asymptotics to Kolmogorov Scaling." Physical Review Letters 74, no. 14 (1995): 2690–93. http://dx.doi.org/10.1103/physrevlett.74.2690.

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Barenblatt, G. I. "Intermediate asymptotics, scaling laws and renormalization group in continuum mechanics." Meccanica 28, no. 3 (1993): 177–83. http://dx.doi.org/10.1007/bf00989119.

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25

Hamm, Andreas. "The Influence of Noise on Fractals." Zeitschrift für Naturforschung A 49, no. 12 (1994): 1238–40. http://dx.doi.org/10.1515/zna-1994-1224.

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Abstract The weak-noise asymptotics of the blurring effect of noise on fractals can be described by scaling laws. It does not only depend on the geometric properties of the fractals but also on their generating dynamics. This is illustrated with the example of the Feigenbaum attractor.

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26

Trofimova, A. A., and A. M. Povolotsky. "Crossover scaling functions in the asymmetric avalanche process." Journal of Physics A: Mathematical and Theoretical 55, no. 2 (2021): 025202. http://dx.doi.org/10.1088/1751-8121/ac3ebb.

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Abstract We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t → ∞ via the Bethe ansatz and a perturbative solution of the TQ-equation. The results are presented in an integral form suitable for the asymptotic analysis in the large system size limit N → ∞. In this limit the first cumulant, the average current per site or the average velo

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27

Abate, Joseph, and Ward Whitt. "Limits and Approximations for the Busy-Period Distribution in Single-Server Queues." Probability in the Engineering and Informational Sciences 9, no. 4 (1995): 581–602. http://dx.doi.org/10.1017/s0269964800004071.

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Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/l queue, the complementary busy-period c.d.f. is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as p → 1), where the scaling parameters are based on the asymptotics as t → ∞. We call this the asymptotic normal approximation, because it involves the standard normal c.d.f. and density. The asymptotic normal approximation is asymptotically correct as t → ∞ for each fixed p and as

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28

Chamecki, Marcelo, Nelson L. Dias, Scott T. Salesky, and Ying Pan. "Scaling Laws for the Longitudinal Structure Function in the Atmospheric Surface Layer." Journal of the Atmospheric Sciences 74, no. 4 (2017): 1127–47. http://dx.doi.org/10.1175/jas-d-16-0228.1.

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Abstract Scaling laws for the longitudinal structure function in the atmospheric surface layer (ASL) are studied using dimensional analysis and matched asymptotics. Theoretical predictions show that the logarithmic scaling for the scales larger than those of the inertial subrange recently proposed for neutral wall-bounded flows also holds for the shear-dominated ASL composed of weakly unstable, neutral, and all stable conditions (as long as continuous turbulence exists). A 2/3 power law is obtained for buoyancy-dominated ASLs. Data from the Advection Horizontal Array Turbulence Study (AHATS) f

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29

Paoletti, Roberto. "Local trace formulae and scaling asymptotics for general quantized Hamiltonian flows." Journal of Mathematical Physics 53, no. 2 (2012): 023501. http://dx.doi.org/10.1063/1.3679660.

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30

Duffield, N. G. "Economies of scale in queues with sources having power-law large deviation scalings." Journal of Applied Probability 33, no. 3 (1996): 840–57. http://dx.doi.org/10.2307/3215363.

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We analyse the queue QL at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian motion (FBM). The workload processes W due to each source are assumed to have large deviation properties of the form P[Wt/a(t) > x] ≈ exp[– v(t)K(x)] for appropriate scaling functions a and v, and rate-function K. Under very general conditions limL→xL–1 log P[QL > Lb] = – I(b), provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic

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31

Duffield, N. G. "Economies of scale in queues with sources having power-law large deviation scalings." Journal of Applied Probability 33, no. 03 (1996): 840–57. http://dx.doi.org/10.1017/s0021900200100257.

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We analyse the queue QL at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian motion (FBM). The workload processes W due to each source are assumed to have large deviation properties of the form P[W t/a(t) &gt; x] ≈ exp[– v(t)K(x)] for appropriate scaling functions a and v, and rate-function K. Under very general conditions lim L→x L –1 log P[QL &gt; Lb] = – I(b), provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the i

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32

Cirillo, Emilio N. M., Ida de Bonis, Adrian Muntean, and Omar Richardson. "Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure." Meccanica 55, no. 11 (2020): 2159–78. http://dx.doi.org/10.1007/s11012-020-01253-8.

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Abstract We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable sc

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Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 3 (2003): 704–20. http://dx.doi.org/10.1239/jap/1059060897.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated

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34

Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 03 (2003): 704–20. http://dx.doi.org/10.1017/s0021900200019653.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated

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35

Ivanova, Ella, Georgii Kalagov, Marina Komarova, and Mikhail Nalimov. "Quantum-Field Multiloop Calculations in Critical Dynamics." Symmetry 15, no. 5 (2023): 1026. http://dx.doi.org/10.3390/sym15051026.

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The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific implementation of the renormalization group program. In recent years, multiloop computation has had a significant breakthrough in both static and dynamic models of critical behavior. In the paper, we focus on the state-of-the-art computational techniques for critical dynamic diagrams and the results obtained with their help. The generic nature of the evaluated physica

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36

van der Hofstad, Remco, and Harsha Honnappa. "Large deviations of bivariate Gaussian extrema." Queueing Systems 93, no. 3-4 (2019): 333–49. http://dx.doi.org/10.1007/s11134-019-09632-z.

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Abstract We establish sharp tail asymptotics for componentwise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the existence of a restricted large deviations principle and identify the unique rate function associated with these asymptotics. Our results identify when the maxima of both coordinates are typically attained by two different versus the same index, and how this depends on the correlation between the coordinates of the bivariate Gaussian random vectors. Our

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37

Goddard, J. V., and S. Naire. "The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate." Journal of Fluid Mechanics 772 (May 7, 2015): 535–68. http://dx.doi.org/10.1017/jfm.2015.212.

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We consider a viscous drop, loaded with an insoluble surfactant, spreading over an inclined plane that is covered initially with a thin surfactant-free liquid film. Lubrication theory is employed to model the flow using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the late-time multi-region asymptotic structure of the spatially one-dimensional spreading flow. A simplified differential–algebraic equation model is derived for key variables characterising the spreading process, using which

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38

Likhanov, Nikolay, and Ravi R. Mazumdar. "Cell loss asymptotics for buffers fed with a large number of independent stationary sources." Journal of Applied Probability 36, no. 1 (1999): 86–96. http://dx.doi.org/10.1239/jap/1032374231.

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In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sourc

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Likhanov, Nikolay, and Ravi R. Mazumdar. "Cell loss asymptotics for buffers fed with a large number of independent stationary sources." Journal of Applied Probability 36, no. 01 (1999): 86–96. http://dx.doi.org/10.1017/s0021900200016867.

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In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sourc

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40

Canzani, Yaiza, and Boris Hanin. "$$C^\infty $$ C ∞ Scaling Asymptotics for the Spectral Projector of the Laplacian." Journal of Geometric Analysis 28, no. 1 (2017): 111–22. http://dx.doi.org/10.1007/s12220-017-9812-5.

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Paoletti, Roberto. "Local Scaling Asymptotics for the Gutzwiller Trace Formula in Berezin–Toeplitz Quantization." Journal of Geometric Analysis 28, no. 2 (2017): 1548–96. http://dx.doi.org/10.1007/s12220-017-9878-0.

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Milišić, Vuk, and Christian Schmeiser. "Asymptotic limits for a nonlinear integro-differential equation modelling leukocytes’ rolling on arterial walls." Nonlinearity 35, no. 2 (2021): 843–69. http://dx.doi.org/10.1088/1361-6544/ac3eb5.

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Abstract We consider a nonlinear integro-differential model describing z, the position of the cell center on the real line presented in Grec et al (2018 J. Theor. Biol. 452 35–46). We introduce a new ɛ-scaling and we prove rigorously the asymptotics when ɛ goes to zero. We show that this scaling characterizes the long-time behavior of the solutions of our problem in the cinematic regime (i.e. the velocity z ˙ tends to a limit). The convergence results are first given when ψ, the elastic energy associated to linkages, is convex and regular (the second order derivative of ψ is bounded). In the a

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43

DEHESA, J. S., A. MARTÍNEZ-FINKELSHTEIN, and V. N. SOROKIN. "SHORT-WAVE ASYMPTOTICS OF THE INFORMATION ENTROPY OF A CIRCULAR MEMBRANE." International Journal of Bifurcation and Chaos 12, no. 11 (2002): 2387–92. http://dx.doi.org/10.1142/s0218127402005935.

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The spreading of the position and momentum probability distributions for the stable free oscillations of a circular membrane of radius l is analyzed by means of the associated Boltzmann–Shannon information entropies in the correspondence principle limit (n → ∞, m fixed), where the numbers (n, m), n ∈ ℕ and m ∈ ℤ, uniquely characterize an oscillation of this two-dimensional system. This is done by solving the short-wave asymptotics of the physical entropies in the two complementary spaces, which boils down to the calculation of the asymptotic behavior of certain entropic integrals of Bessel fun

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44

Hnatich, M., and D. Horváth. "Modified Self-Scaling Relation for the Inertial and Low Energy Containing Scales of Decaying Turbulence." International Journal of Modern Physics B 12, no. 04 (1998): 405–31. http://dx.doi.org/10.1142/s0217979298000272.

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The limits of a new form of scaling, named Extended Self Similarity (ESS) originally suggested [R. Benzi et al., Phys. Rev.E48 (1993), 29] for the inertial, dissipation and transition scales are discussed. A modification of the ESS concept is put forward using the model of decaying turbulence at high Reynolds numbers [L. Ts. Adzhemyan et al., Czech. J. Phys.45 (1995), 517]. In this model the statistical description is simplified by the hypotheses of homogeneity, isotropy, incompressibility and self-similarity, for the power law stage of decay the presence of a single scaling length — Karman sc

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45

Antonov, N. V., A. N. Vasil'ev, and A. S. Stepanenko. "Scaling function ??0 asymptotics of the correlation function in theO n ?4 model." Theoretical and Mathematical Physics 88, no. 1 (1991): 779–81. http://dx.doi.org/10.1007/bf01016349.

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46

Fong, Silas, and Vincent Tan. "Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel." Entropy 19, no. 7 (2017): 364. http://dx.doi.org/10.3390/e19070364.

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Bakhtin, Yuri, and Andrzej Święch. "Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations." Transactions of the American Mathematical Society 368, no. 9 (2015): 6487–517. http://dx.doi.org/10.1090/tran/6574.

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CHAVES, MANUELA, and VICTOR A. GALAKTIONOV. "LYAPUNOV FUNCTIONALS IN SINGULAR LIMITS FOR PERTURBED QUASILINEAR DEGENERATE PARABOLIC EQUATIONS." Analysis and Applications 01, no. 04 (2003): 351–85. http://dx.doi.org/10.1142/s0219530503000193.

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As a key example, we study the asymptotic behaviour near finite focusing time t=T of radial solutions of the porous medium equation with absorption [Formula: see text] with bounded compactly supported initial data u(x,0)=u0(|x|), and exponents m>1 and p>pc, where pc=pc(m,N)∈(-m,0) is a critical exponent. We show that under certain assumptions, the behaviour of the solution as t→T- near the origin is described by self-similar Graveleau solutions of the porous medium equation ut=Δum. In the rescaled variables, we deal with an exponential non-autonomous perturbation of a quasilinear parabol

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Laarhoven, Thijs. "Approximate Voronoi cells for lattices, revisited." Journal of Mathematical Cryptology 15, no. 1 (2020): 60–71. http://dx.doi.org/10.1515/jmc-2020-0074.

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AbstractWe revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis–Laarhoven–De Weger [PQCrypto, 2019] of determining exact asymptotics on the volume of these Voronoi cells under the Gaussian heuristic. As a result, we obtain improved upper bounds on the time complexity of the randomized iterative slicer when using less than $2^{0.076d + o(d)}$ memory, and we show how to obtain time–memory trade-offs even when using less than $2^{0.048d + o(d)}$ memory. We also settl

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DREHER, FABIAN, and MARC KESSEBÖHMER. "Escape rates for special flows and their higher order asymptotics." Ergodic Theory and Dynamical Systems 39, no. 06 (2017): 1501–30. http://dx.doi.org/10.1017/etds.2017.76.

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In this paper escape rates and local escape rates for special flows are studied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfils certain scaling, invariance and continuity properties. In the context of metric spaces local escape rates are considered. If the base transformation is ergodic and exhibits an exponential convergence in probability of ergodic sums, then the local escape rate with respect to the flow is just the local escape rate with respect to the base transformation, divided by the integral of the ceiling funct

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