Zeitschriftenartikel: „Dynamical large deviations“

1

Young, Lai-Sang. „Large deviations in dynamical systems“. Transactions of the American Mathematical Society 318, Nr. 2 (01.02.1990): 525–43. http://dx.doi.org/10.1090/s0002-9947-1990-0975689-7.

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2

Wu, Xinxing, Xiong Wang und Guanrong Chen. „On the Large Deviations Theorem of Weaker Types“. International Journal of Bifurcation and Chaos 27, Nr. 08 (Juli 2017): 1750127. http://dx.doi.org/10.1142/s0218127417501279.

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In this paper, we introduce the concepts of the large deviations theorem of weaker types, i.e. type I, type I[Formula: see text], type II, type II[Formula: see text], type III, and type III[Formula: see text], and present a systematic study of the ergodic and chaotic properties of dynamical systems satisfying the large deviations theorem of various types. Some characteristics of the ergodic measure are obtained and then applied to prove that every dynamical system satisfying the large deviations theorem of type I[Formula: see text] is ergodic, which is equivalent to the large deviations theorem of type II[Formula: see text] in this regard, and that every uniquely ergodic dynamical system restricted on its support satisfies the large deviations theorem. Moreover, we prove that every dynamical system satisfying the large deviations theorem of type III is an [Formula: see text]-system.

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3

Bogenschütz, Thomas, und Achim Doebler. „Large deviations in expanding random dynamical systems“. Discrete & Continuous Dynamical Systems - A 5, Nr. 4 (1999): 805–12. http://dx.doi.org/10.3934/dcds.1999.5.805.

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4

Kleptsyn, Victor, Dmitry Ryzhov und Stanislav Minkov. „Special ergodic theorems and dynamical large deviations“. Nonlinearity 25, Nr. 11 (15.10.2012): 3189–96. http://dx.doi.org/10.1088/0951-7715/25/11/3189.

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5

Kifer, Yuri. „Averaging in dynamical systems and large deviations“. Inventiones Mathematicae 110, Nr. 1 (Dezember 1992): 337–70. http://dx.doi.org/10.1007/bf01231336.

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6

Whitelam, Stephen, Daniel Jacobson und Isaac Tamblyn. „Evolutionary reinforcement learning of dynamical large deviations“. Journal of Chemical Physics 153, Nr. 4 (28.07.2020): 044113. http://dx.doi.org/10.1063/5.0015301.

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7

ARAÚJO, VÍTOR, und ALEXANDER I. BUFETOV. „A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials“. Ergodic Theory and Dynamical Systems 31, Nr. 4 (20.07.2010): 1043–71. http://dx.doi.org/10.1017/s0143385710000349.

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AbstractLarge deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

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8

REY-BELLET, LUC, und LAI-SANG YOUNG. „Large deviations in non-uniformly hyperbolic dynamical systems“. Ergodic Theory and Dynamical Systems 28, Nr. 2 (April 2008): 587–612. http://dx.doi.org/10.1017/s0143385707000478.

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AbstractWe prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hénon-type attractors.

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9

Kifer, Yuri. „Large deviations in dynamical systems and stochastic processes“. Transactions of the American Mathematical Society 321, Nr. 2 (01.02.1990): 505–24. http://dx.doi.org/10.1090/s0002-9947-1990-1025756-7.

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10

Touchette, Hugo. „Introduction to dynamical large deviations of Markov processes“. Physica A: Statistical Mechanics and its Applications 504 (August 2018): 5–19. http://dx.doi.org/10.1016/j.physa.2017.10.046.

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11

Budhiraja, Amarjit, Paul Dupuis und Vasileios Maroulas. „Large deviations for infinite dimensional stochastic dynamical systems“. Annals of Probability 36, Nr. 4 (Juli 2008): 1390–420. http://dx.doi.org/10.1214/07-aop362.

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12

Melbourne, Ian. „Large and moderate deviations for slowly mixing dynamical systems“. Proceedings of the American Mathematical Society 137, Nr. 05 (26.11.2008): 1735–41. http://dx.doi.org/10.1090/s0002-9939-08-09751-7.

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13

Kifer, Yuri. „Large deviations, averaging and periodic orbits of dynamical systems“. Communications in Mathematical Physics 162, Nr. 1 (April 1994): 33–46. http://dx.doi.org/10.1007/bf02105185.

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14

Wu, Xinxing, und Xiong Wang. „On the Iteration Properties of Large Deviations Theorem“. International Journal of Bifurcation and Chaos 26, Nr. 03 (März 2016): 1650054. http://dx.doi.org/10.1142/s0218127416500541.

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An important feature of chaoticity of a dynamical system [Formula: see text] is its sensitive dependence on initial conditions, which has recently been extended to a concept of ergodic sensitivity. This paper proves that if there exists a positive integer [Formula: see text] such that [Formula: see text] satisfies the large deviations theorem or ergodicity, then so is [Formula: see text]. Moreover, the iteration invariance of some ergodic properties are obtained.

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15

Ignatiouk-Robert, I. „Large deviations for a random walk in dynamical random environment“. Annales de l'Institut Henri Poincare (B) Probability and Statistics 34, Nr. 5 (Oktober 1998): 601–36. http://dx.doi.org/10.1016/s0246-0203(98)80002-2.

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16

KIFER, YURI. „Averaging principle for fully coupled dynamical systems and large deviations“. Ergodic Theory and Dynamical Systems 24, Nr. 3 (Juni 2004): 847–71. http://dx.doi.org/10.1017/s014338570400001x.

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17

Landim, C., und K. Tsunoda. „Hydrostatics and dynamical large deviations for a reaction-diffusion model“. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, Nr. 1 (Februar 2018): 51–74. http://dx.doi.org/10.1214/16-aihp794.

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18

Lazarescu, Alexandre, Tommaso Cossetto, Gianmaria Falasco und Massimiliano Esposito. „Large deviations and dynamical phase transitions in stochastic chemical networks“. Journal of Chemical Physics 151, Nr. 6 (14.08.2019): 064117. http://dx.doi.org/10.1063/1.5111110.

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19

VARANDAS, PAULO, und YUN ZHAO. „Weak specification properties and large deviations for non-additive potentials“. Ergodic Theory and Dynamical Systems 35, Nr. 3 (09.10.2013): 968–93. http://dx.doi.org/10.1017/etds.2013.66.

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AbstractWe obtain large deviation bounds for the measure of deviation sets associated with asymptotically additive and sub-additive potentials under some weak specification properties. In particular, a large deviation principle is obtained in the case of uniformly hyperbolic dynamical systems. Some applications to the study of the convergence of Lyapunov exponents are given.

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20

Nicol, Matthew, und Andrew Török. „A note on large deviations for unbounded observables“. Stochastics and Dynamics 20, Nr. 05 (26.12.2019): 2050030. http://dx.doi.org/10.1142/s0219493720500306.

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We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the tail behavior of the cumulative distribution function. We give examples of unbounded observables with exponential decay of autocorrelations, exponential decay under the transfer operator in each [Formula: see text], [Formula: see text], and strictly stretched exponential large deviation. For observables of form [Formula: see text], [Formula: see text] periodic, on uniformly expanding systems we give the precise stretched exponential decay rate. We also show that a classical example in the literature of a bounded observable with exponential decay of autocorrelations yet with no rate function is degenerate as the observable is a coboundary.

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21

Gouëzel, Sébastien. „Correlation asymptotics from large deviations in dynamical systems with infinite measure“. Colloquium Mathematicum 125, Nr. 2 (2011): 193–212. http://dx.doi.org/10.4064/cm125-2-5.

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22

Aimino, Romain, und Jorge Milhazes Freitas. „Large deviations for dynamical systems with stretched exponential decay of correlations“. Portugaliae Mathematica 76, Nr. 2 (13.02.2020): 143–52. http://dx.doi.org/10.4171/pm/2030.

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23

Tang, Yanjie, und Jiandong Yin. „The dynamics of nonautonomous dynamical systems with the large deviations theorem“. Dynamical Systems 36, Nr. 3 (03.06.2021): 416–26. http://dx.doi.org/10.1080/14689367.2021.1926430.

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24

Bertini, Lorenzo, Claudio Landim und Mustapha Mourragui. „Dynamical large deviations for the boundary driven weakly asymmetric exclusion process“. Annals of Probability 37, Nr. 6 (November 2009): 2357–403. http://dx.doi.org/10.1214/09-aop472.

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25

Lepri, Stefano. „Large-deviations approach to thermalization: the case of harmonic chains with conservative noise“. Journal of Statistical Mechanics: Theory and Experiment 2024, Nr. 7 (26.07.2024): 073208. http://dx.doi.org/10.1088/1742-5468/ad6135.

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Abstract We investigate the possibility of characterizing the different thermalization pathways through a large-deviation approach. Specifically, we consider clean, disordered and quasi-periodic harmonic chains under energy and momentum-conserving noise. For their associated master equations, describing the dynamics of normal modes energies, we compute the fluctuations of activity and dynamical entropy in the corresponding biased ensembles. First-order dynamical phase transition are found that originates from different activity regions in action space. At the transitions, the steady-state in the biased ensembles changes from extended to localized, yielding a kind of condensation in normal-modes space. For the disordered and quasi-periodic models, we argue that the phase-diagram has a critical point at a finite value of the disorder or potential strength.

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26

Kifer, Yuri. „Erdős–Rényi law of large numbers in the averaging setup“. Stochastics and Dynamics 18, Nr. 03 (18.05.2018): 1850018. http://dx.doi.org/10.1142/s0219493718500181.

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We extend the Erdős–Rényi law of large numbers to the averaging setup both in discrete and continuous time cases. We consider both stochastic processes and dynamical systems as fast motions whenever they are fast mixing and satisfy large deviations estimates. In the continuous time case we consider flows with large deviations estimates which allow a suspension representation and it turns out that fast mixing of corresponding base transformations suffices for our results.

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27

Hu, Shulan, und Liming Wu. „Large deviations for random dynamical systems and applications to hidden Markov models“. Stochastic Processes and their Applications 121, Nr. 1 (Januar 2011): 61–90. http://dx.doi.org/10.1016/j.spa.2010.07.003.

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28

Farfan, J., C. Landim und M. Mourragui. „Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusion processes“. Stochastic Processes and their Applications 121, Nr. 4 (April 2011): 725–58. http://dx.doi.org/10.1016/j.spa.2010.11.014.

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29

Dedecker, Jérôme, Sébastien Gouëzel und Florence Merlevède. „Large and moderate deviations for bounded functions of slowly mixing Markov chains“. Stochastics and Dynamics 18, Nr. 02 (11.12.2017): 1850017. http://dx.doi.org/10.1142/s021949371850017x.

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We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.

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30

Gabrielli, Davide, und D. R. Michiel Renger. „Dynamical Phase Transitions for Flows on Finite Graphs“. Journal of Statistical Physics 181, Nr. 6 (17.11.2020): 2353–71. http://dx.doi.org/10.1007/s10955-020-02667-0.

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AbstractWe study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.

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31

Seol, Youngsoo. „Large Deviations for Hawkes Processes with Randomized Baseline Intensity“. Mathematics 11, Nr. 8 (12.04.2023): 1826. http://dx.doi.org/10.3390/math11081826.

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The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with a clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of self-exciting point processes, the Hawkes model is generally not Markovian. In certain special circumstances, it can be Markovian with a generator of the model if the exciting function is an exponential function or the sum of exponential functions. In the case of non-Markovian processes, difficulties arise when the exciting function is not an exponential function or a sum of exponential functions. The intensity of the Hawkes process is given by the sum of a baseline intensity and other terms that depend on the entire history of the point process, as compared to a standard Poisson process. It is one of the main methods used for studying the dynamical properties of general point processes, and is highly important for credit risk studies. The baseline intensity, which is instrumental in the Hawkes model, is usually defined for deterministic cases. In this paper, we consider a linear Hawkes model where the baseline intensity is randomly defined, and investigate the asymptotic results of the large deviations principle for the newly defined model. The Hawkes processes with randomized baseline intensity, dealt with in this paper, have wide applications in insurance, finance, queue theory, and statistics.

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32

Mourragui, Mustapha, und Enza Orlandi. „Boundary driven Kawasaki process with long-range interaction: dynamical large deviations and steady states“. Nonlinearity 26, Nr. 1 (19.11.2012): 141–75. http://dx.doi.org/10.1088/0951-7715/26/1/141.

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33

Meson, Alejandro M., und Fernando Vericat. „On Large Deviations for Some Dynamical Systems and for Gibbs States at Zero Temperature“. Journal of Dynamical Systems and Geometric Theories 9, Nr. 2 (November 2011): 151–64. http://dx.doi.org/10.1080/1726037x.2011.10698598.

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34

Maroulas, Vasileios, Xiaoyang Pan und Jie Xiong. „Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise“. Stochastic Processes and their Applications 130, Nr. 1 (Januar 2020): 203–31. http://dx.doi.org/10.1016/j.spa.2019.02.009.

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35

Franco, Tertuliano, Patricia Gonçalves, Claudio Landim und Adriana Neumann. „Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions“. Latin American Journal of Probability and Mathematical Statistics 19, Nr. 2 (2022): 1497. http://dx.doi.org/10.30757/alea.v19-60.

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36

Pfister, C.-E., und W. G. Sullivan. „Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts“. Nonlinearity 18, Nr. 1 (09.10.2004): 237–61. http://dx.doi.org/10.1088/0951-7715/18/1/013.

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37

Jack, Robert L., und Peter Sollich. „Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories“. Journal of Physics A: Mathematical and Theoretical 47, Nr. 1 (03.12.2013): 015003. http://dx.doi.org/10.1088/1751-8113/47/1/015003.

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38

Farfan, Jonathan, Alexandre B. Simas und Fábio J. Valentim. „Dynamical Large Deviations for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities“. Journal of Statistical Physics 139, Nr. 4 (03.04.2010): 658–85. http://dx.doi.org/10.1007/s10955-010-9957-0.

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39

Kifer, Yuri. „Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging“. Memoirs of the American Mathematical Society 201, Nr. 944 (2009): 0. http://dx.doi.org/10.1090/memo/0944.

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40

WANG, QIUDONG, und LAI-SANG YOUNG. „Dynamical profile of a class of rank-one attractors“. Ergodic Theory and Dynamical Systems 33, Nr. 4 (08.05.2012): 1221–64. http://dx.doi.org/10.1017/s014338571200020x.

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AbstractThis paper contains results on the geometric and ergodic properties of a class of strange attractors introduced by Wang and Young [Towards a theory of rank one attractors. Ann. of Math. (2) 167 (2008), 349–480]. These attractors can live in phase spaces of any dimension, and have been shown to arise naturally in differential equations that model several commonly occurring phenomena. Dynamically, such systems are chaotic; they have controlled non-uniform hyperbolicity with exactly one unstable direction, hence the name rank-one. In this paper we prove theorems on their Lyapunov exponents, Sinai–Ruelle–Bowen (SRB) measures, basins of attraction, and statistics of time series, including central limit theorems, exponential correlation decay and large deviations. We also present results on their global geometric and combinatorial structures, symbolic coding and periodic points. In short, we build a dynamical profile for this class of dynamical systems, proving that these systems exhibit many of the characteristics normally associated with ‘strange attractors’.

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41

Kato, Seiji. „Interannual Variability of the Global Radiation Budget“. Journal of Climate 22, Nr. 18 (15.09.2009): 4893–907. http://dx.doi.org/10.1175/2009jcli2795.1.

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Abstract Interannual variability of the global radiation budget, regions that contribute to its variability, and what limits albedo variability are investigated using Clouds and the Earth’s Radiant Energy System (CERES) data taken from March 2000 through February 2004. Area-weighted mean top-of-atmosphere (TOA) reflected shortwave, longwave, and net irradiance standard deviations computed from monthly anomalies over a 1° × 1° region are 9.6, 7.6, and 7.6 W m−2, respectively. When standard deviations are computed from global monthly anomalies, they drop to 0.5, 0.4, and 0.4 W m−2, respectively. Clouds are mostly responsible for the variation. Regions with a large standard deviation of TOA shortwave and longwave irradiance at TOA are the tropical western and central Pacific, which is caused by shifting from La Niña to El Niño during this period. However, a larger standard deviation of 300–1000-hPa thickness anomalies occurs in the polar region instead of the tropics. The correlation coefficient between atmospheric net irradiance anomalies and 300–1000-hPa thickness anomalies is negative. These indicate that temperature anomalies in the atmosphere are mostly a result of anomalies in longwave and dynamical processes that transport energy poleward, instead of albedo anomalies by clouds directly affecting temperature anomalies in the atmosphere. With simple zonal-mean thermodynamic energy equations it is demonstrated that temperature anomalies decay exponentially with time by longwave emission and by dynamical processes. As a result, the mean meridional temperature gradient is maintained. Therefore, mean meridional circulations are not greatly altered by albedo anomalies on an annual time scale, which in turn provides small interannual variability of the global mean albedo.

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42

Monthus, Cécile. „Large deviations for dynamical fluctuations of open Markov processes, with application to random cascades on trees“. Journal of Physics A: Mathematical and Theoretical 52, Nr. 2 (10.12.2018): 025001. http://dx.doi.org/10.1088/1751-8121/aaf141.

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43

Michel, Julien, und Raoul Robert. „Large deviations for young measures and statistical mechanics of infinite dimensional dynamical systems with conservation law“. Communications in Mathematical Physics 159, Nr. 1 (Januar 1994): 195–215. http://dx.doi.org/10.1007/bf02100491.

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44

FREIDLIN, MARK. „ON STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS WITH FAST AND SLOW COMPONENTS“. Stochastics and Dynamics 01, Nr. 02 (Juni 2001): 261–81. http://dx.doi.org/10.1142/s0219493701000138.

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Dynamical systems with fast and slow components are considered. We show that small random perturbations of the fast component can lead to essential changes in the limiting slow motion. For example, new stable equilibria or deterministic oscillations with amplitude and frequency of order 1 can be introduced by the perturbations. These are stochastic resonance type effects, and they are considered from the point of view of large deviations theory.

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45

Zhang, Guowei. „The lower bound on the measure of sets consisting of Julia limiting directions of solutions to some complex equations associated with Petrenko's deviation“. AIMS Mathematics 8, Nr. 9 (2023): 20169–86. http://dx.doi.org/10.3934/math.20231028.

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<abstract><p>In the value distribution theory of complex analysis, Petrenko's deviation is to describe more precisely the quantitative relationship between $ T (r, f) $ and $ \log M (r, f) $ when the modulus of variable $ |z| = r $ is sufficiently large. In this paper we introduce Petrenko's deviations to the coefficients of three types of complex equations, which include difference equations, differential equations and differential-difference equations. Under different assumptions we study the lower bound of limiting directions of Julia sets of solutions of these equations, where Julia set is an important concept in complex dynamical systems. The results of this article show that the lower bound of limiting directions mentioned above is closely related to Petrenko's deviation, and our conclusions improve some known results.</p></abstract>

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46

Haderlein, Karin, David J. Luitz, Corinna Kollath und Ameneh Sheikhan. „Level statistics of the one-dimensional dimerized Hubbard model“. Journal of Statistical Mechanics: Theory and Experiment 2024, Nr. 7 (05.07.2024): 073101. http://dx.doi.org/10.1088/1742-5468/ad5270.

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Abstract The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

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47

ATHREYA, AVANTI, und MARK FREIDLIN. „METASTABILITY FOR RANDOM PERTURBATIONS OF NEARLY-HAMILTONIAN SYSTEMS“. Stochastics and Dynamics 08, Nr. 01 (März 2008): 1–21. http://dx.doi.org/10.1142/s0219493708002172.

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We characterize the phenomenon of metastability for a small random perturbation of a nearly-Hamiltonian dynamical system. We use the averaging principle and the theory of large deviations to prove that the metastable "state" is, in general, not a single state but rather a nondegenerate probability measure across the stable equilibrium points of the unperturbed Hamiltonian system. The set of all possible "metastable distributions" is a finite set that is independent of the stochastic perturbation.

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48

Pardoux, Etienne, und Brice Samegni-Kepgnou. „Large deviations of the exit measure through a characteristic boundary for a Poisson driven SDE“. ESAIM: Probability and Statistics 24 (2020): 148–85. http://dx.doi.org/10.1051/ps/2019031.

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Let O be the basin of attraction of a given equilibrium of a dynamical system, whose solution is the law of large numbers limit of the solution of a Poissonian SDE as the size of the population tends to +∞. We consider the law of the exit point from O of that Poissonian SDE. We adapt the approach of Day [J. Math. Anal. Appl. 147 (1990) 134–153] who studied the same problem for an ODE with a small Brownian perturbation. For that purpose, we will use the large deviations principle for the Poissonian SDE reflected at the boundary of O, studied in our recent work Pardoux and Samegni [Stoch. Anal. Appl. 37 (2019) 836–864]. The main motivation of this work is the extension of the results concerning the time of exit from the set O established in Kratz and Pardoux [Vol. 2215 of Lecture Notes in Math.. Springer (2018) 221–327] and Pardoux and Samegni [J. Appl. Probab. 54 (2017) 905–920] to unbounded open sets O. This is done in sections 4.2.5 and 4.2.7 of Britton and Pardoux [Vol. 2255 of Lecture Notes in Math. Springer (2019) 1–120], see also The SIR model with demography subsection below.

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49

Ferreira, Hermes H., Artur O. Lopes und Silvia R. C. Lopes. „Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests“. Journal of Dynamics and Games 9, Nr. 2 (2022): 123. http://dx.doi.org/10.3934/jdg.2021031.

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<p style='text-indent:20px;'>We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different Hölder Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially better, compared to other alternative tests, when the sample size goes to infinity. We are able to present the explicit exponential decay rate. We also consider both, the Min-Max and a certain type of Bayesian hypotheses tests. We shall consider these tests in the log likelihood framework by using several tools of Thermodynamic Formalism. Versions of the Stein's Lemma and Chernoff's information are also presented.</p>

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BROOIJMANS, GUSTAAF. „SEARCHES FOR NEW PHYSICS“. International Journal of Modern Physics A 20, Nr. 14 (10.06.2005): 3033–49. http://dx.doi.org/10.1142/s0217751x05025711.

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Current experimental limits for new physics beyond the Standard Model and hints for deviations from Standard Model expectations will be reviewed, highlighting recent results. Possible signals that will be discussed include Higgs bosons, supersymmetric particles, large extra dimensions, new gauge bosons, dynamical symmetry breaking, muon g - 2, rare decays and lepton flavor violation. The discovery potential of the LHC and ILC will be presented, and the impact of discovery on answering fundamental questions of physics will be assessed.

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