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Journal articles on the topic 'Percolation de dernier passage'

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Published: 23 September 2022
Last updated: 28 September 2022

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1

Kesten, Harry. "Percolation Theory and First-Passage Percolation." Annals of Probability 15, no. 4 (October 1987): 1231–71. http://dx.doi.org/10.1214/aop/1176991975.

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2

Hoffman, Christopher. "Geodesics in first passage percolation." Annals of Applied Probability 18, no. 5 (October 2008): 1944–69. http://dx.doi.org/10.1214/07-aap510.

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3

Berger, Quentin, and Niccolò Torri. "Entropy-controlled Last-Passage Percolation." Annals of Applied Probability 29, no. 3 (June 2019): 1878–903. http://dx.doi.org/10.1214/18-aap1448.

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4

Licea, C., C. M. Newman, and M. S. T. Piza. "Superdiffusivity in first-passage percolation." Probability Theory and Related Fields 106, no. 4 (December 13, 1996): 559–91. http://dx.doi.org/10.1007/s004400050075.

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5

Damron, Michael, and Jack Hanson. "Bigeodesics in First-Passage Percolation." Communications in Mathematical Physics 349, no. 2 (September 22, 2016): 753–76. http://dx.doi.org/10.1007/s00220-016-2743-3.

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6

López, Sergio I., and Leandro P. R. Pimentel. "Geodesic forests in last-passage percolation." Stochastic Processes and their Applications 127, no. 1 (January 2017): 304–24. http://dx.doi.org/10.1016/j.spa.2016.06.009.

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7

Yukich, J. E., and Yu Zhang. "Singularity points for first passage percolation." Annals of Probability 34, no. 2 (March 2006): 577–92. http://dx.doi.org/10.1214/009117905000000819.

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8

Kesten, Harry, and Vladas Sidoravicius. "A problem in last-passage percolation." Brazilian Journal of Probability and Statistics 24, no. 2 (July 2010): 300–320. http://dx.doi.org/10.1214/09-bjps032.

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9

Andjel, Enrique D., and Maria E. Vares. "First passage percolation and escape strategies." Random Structures & Algorithms 47, no. 3 (May 23, 2014): 414–23. http://dx.doi.org/10.1002/rsa.20548.

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10

Zhang, Yu, and Yunshyong Chow. "Large deviations in first-passage percolation." Annals of Applied Probability 13, no. 4 (November 2003): 1601–14. http://dx.doi.org/10.1214/aoap/1069786513.

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11

Comets, Francis, Jeremy Quastel, and Alejandro F. Ramírez. "Last Passage Percolation and Traveling Fronts." Journal of Statistical Physics 152, no. 3 (June 21, 2013): 419–51. http://dx.doi.org/10.1007/s10955-013-0779-8.

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12

Zhang, Yu. "Supercritical behaviors in first-passage percolation." Stochastic Processes and their Applications 59, no. 2 (October 1995): 251–66. http://dx.doi.org/10.1016/0304-4149(95)00051-8.

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13

Hambly, Ben, and James B. Martin. "Heavy tails in last-passage percolation." Probability Theory and Related Fields 137, no. 1-2 (September 20, 2006): 227–75. http://dx.doi.org/10.1007/s00440-006-0019-0.

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14

Betea, Dan, Patrik L. Ferrari, and Alessandra Occelli. "Stationary Half-Space Last Passage Percolation." Communications in Mathematical Physics 377, no. 1 (March 9, 2020): 421–67. http://dx.doi.org/10.1007/s00220-020-03712-5.

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15

Howard, C. Douglas, and Charles M. Newman. "Euclidean models of first-passage percolation." Probability Theory and Related Fields 108, no. 2 (June 4, 1997): 153–70. http://dx.doi.org/10.1007/s004400050105.

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16

Dhar, D. "First passage percolation in many dimensions." Physics Letters A 130, no. 4-5 (July 1988): 308–10. http://dx.doi.org/10.1016/0375-9601(88)90616-0.

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17

Boivin, Daniel. "First passage percolation: The stationary case." Probability Theory and Related Fields 86, no. 4 (December 1990): 491–99. http://dx.doi.org/10.1007/bf01198171.

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18

Basu, Riddhipratim, and Mahan Mj. "First passage percolation on hyperbolic groups." Advances in Mathematics 408 (October 2022): 108599. http://dx.doi.org/10.1016/j.aim.2022.108599.

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19

Alberts, Tom, and Eric Cator. "On the Passage Time Geometry of the Last Passage Percolation Problem." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 211. http://dx.doi.org/10.30757/alea.v18-10.

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20

Cerf, Raphaël, and Marie Théret. "Weak shape theorem in first passage percolation with infinite passage times." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 52, no. 3 (August 2016): 1351–81. http://dx.doi.org/10.1214/15-aihp686.

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21

Herrndorf, Norbert. "First-passage percolation processes with finite height." Journal of Applied Probability 22, no. 4 (December 1985): 766–75. http://dx.doi.org/10.2307/3213944.

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We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.
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22

Kolossváry, István, and Júlia Komjáthy. "First Passage Percolation on Inhomogeneous Random Graphs." Advances in Applied Probability 47, no. 02 (June 2015): 589–610. http://dx.doi.org/10.1017/s0001867800007990.

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In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobáset al.(2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃nof a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidiet al.(2011), where first passage percolation is explored on the Erdős-Rényi graphs.
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23

Wang, Feng, Xian-Yuan Wu, and Rui Zhu. "Last passage percolation on the complete graph." Statistics & Probability Letters 164 (September 2020): 108798. http://dx.doi.org/10.1016/j.spl.2020.108798.

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24

Bernstein, Megan, Michael Damron, and Torin Greenwood. "Sublinear variance in Euclidean first-passage percolation." Stochastic Processes and their Applications 130, no. 8 (August 2020): 5060–99. http://dx.doi.org/10.1016/j.spa.2020.02.011.

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25

Herrndorf, Norbert. "First-passage percolation processes with finite height." Journal of Applied Probability 22, no. 04 (December 1985): 766–75. http://dx.doi.org/10.1017/s0021900200108009.

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We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.
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26

Licea, Cristina, and Charles M. Newman. "Geodesics in two-dimensional first-passage percolation." Annals of Probability 24, no. 1 (1996): 399–410. http://dx.doi.org/10.1214/aop/1042644722.

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27

Schramm, Oded, Gil Kalai, and Itai Benjamini. "First passage percolation has sublinear distance variance." Annals of Probability 31, no. 4 (October 2003): 1970–78. http://dx.doi.org/10.1214/aop/1068646373.

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28

Haggstrom, Olle, and Ronald Meester. "Asymptotic Shapes for Stationary First Passage Percolation." Annals of Probability 23, no. 4 (October 1995): 1511–22. http://dx.doi.org/10.1214/aop/1176987792.

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29

van der Hofstad, Remco, Gerard Hooghiemstra, and Piet Van Mieghem. "FIRST-PASSAGE PERCOLATION ON THE RANDOM GRAPH." Probability in the Engineering and Informational Sciences 15, no. 2 (April 2001): 225–37. http://dx.doi.org/10.1017/s026996480115206x.

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30

Damron, Michael, Wai-Kit Lam, and Xuan Wang. "Asymptotics for $2D$ critical first passage percolation." Annals of Probability 45, no. 5 (September 2017): 2941–70. http://dx.doi.org/10.1214/16-aop1129.

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31

Yeliussizov, Damir. "Dual Grothendieck polynomials via last-passage percolation." Comptes Rendus. Mathématique 358, no. 4 (July 28, 2020): 497–503. http://dx.doi.org/10.5802/crmath.67.

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32

Rolla, Leonardo, and Augusto Teixeira. "Last Passage Percolation in Macroscopically Inhomogeneous Media." Electronic Communications in Probability 13 (2008): 131–39. http://dx.doi.org/10.1214/ecp.v13-1287.

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33

Martinsson, Anders. "First-passage percolation on Cartesian power graphs." Annals of Probability 46, no. 2 (March 2018): 1004–41. http://dx.doi.org/10.1214/17-aop1199.

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34

Takei, Masato. "A note on anisotropic first-passage percolation." Journal of Mathematics of Kyoto University 46, no. 4 (2006): 903–12. http://dx.doi.org/10.1215/kjm/1250281609.

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35

Kolossváry, István, and Júlia Komjáthy. "First Passage Percolation on Inhomogeneous Random Graphs." Advances in Applied Probability 47, no. 2 (June 2015): 589–610. http://dx.doi.org/10.1239/aap/1435236989.

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Abstract:
In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobás et al. (2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃n of a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidi et al. (2011), where first passage percolation is explored on the Erdős-Rényi graphs.
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36

Ikhlef, Yacine, and Anita K. Ponsaing. "Finite-Size Left-Passage Probability in Percolation." Journal of Statistical Physics 149, no. 1 (September 7, 2012): 10–36. http://dx.doi.org/10.1007/s10955-012-0573-z.

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37

Calder, Jeff. "Directed Last Passage Percolation with Discontinuous Weights." Journal of Statistical Physics 158, no. 4 (November 18, 2014): 903–49. http://dx.doi.org/10.1007/s10955-014-1146-0.

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38

Maga, B. "Baire categorical aspects of first passage percolation." Acta Mathematica Hungarica 156, no. 1 (May 25, 2018): 145–71. http://dx.doi.org/10.1007/s10474-018-0840-9.

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39

Rota, Gian-Carlo. "First-passage percolation on the square lattice." Advances in Mathematics 57, no. 2 (August 1985): 208. http://dx.doi.org/10.1016/0001-8708(85)90059-3.

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40

Graham, B. T. "Sublinear Variance for Directed Last-Passage Percolation." Journal of Theoretical Probability 25, no. 3 (October 6, 2010): 687–702. http://dx.doi.org/10.1007/s10959-010-0315-6.

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41

Martin, James B. "Batch queues, reversibility and first-passage percolation." Queueing Systems 62, no. 4 (August 2009): 411–27. http://dx.doi.org/10.1007/s11134-009-9137-6.

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42

Alexander, Kenneth S., and Quentin Berger. "Geodesics Toward Corners in First Passage Percolation." Journal of Statistical Physics 172, no. 4 (June 20, 2018): 1029–56. http://dx.doi.org/10.1007/s10955-018-2088-8.

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43

Balázs, Márton, Ofer Busani, and Timo Seppäläinen. "Local stationarity in exponential last-passage percolation." Probability Theory and Related Fields 180, no. 1-2 (March 15, 2021): 113–62. http://dx.doi.org/10.1007/s00440-021-01035-7.

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AbstractWe consider point-to-point last-passage times to every vertex in a neighbourhood of size $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on $$\delta $$ δ . Through this result we show that (1) the $$\text {Airy}_2$$ Airy 2 process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of side length $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 going to a point at distance N agrees inside the box with the tree of semi-infinite geodesics going in the same direction; (3) two point-to-point geodesics started at distance $$N^{\nicefrac {2}{3}}$$ N 2 3 from each other, to a point at distance N, will not coalesce close to either endpoint on the scale N. Our main results rely on probabilistic methods only.
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44

Lachal, Aimé. "Dernier instant de passage pour l'intégrale du mouvement brownien." Stochastic Processes and their Applications 49, no. 1 (January 1994): 57–64. http://dx.doi.org/10.1016/0304-4149(94)90111-2.

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45

GASCON, F., and A. GALVAN. "THE STUDY OF PHOTON TRANSMISSION IN THE FABRY-PEROT INTERFEROMETER." Fractals 07, no. 02 (June 1999): 169–79. http://dx.doi.org/10.1142/s0218348x99000190.

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This paper aims to study the phenomenon of light transmission through an interferometer by considering the passage of photons through the plates as a phenomenon of fractal percolation. In addition to the percolation of contacts, porous percolation, the percolation of points and the percolation of rebounds are also studied here (in the form described below).
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46

Chayes, L., and C. Winfield. "The density of interfaces: a new first-passage problem." Journal of Applied Probability 30, no. 04 (December 1993): 851–62. http://dx.doi.org/10.1017/s0021900200044612.

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We introduce and study a novel type of first-passage percolation problem onwhere the associated first-passage time measures the density of interface between two types of sites. If the types, designated + and –, are independently assigned their values with probabilitypand (1 —p) respectively, we show that the density of interface is non-zero provided that both species are subcritical with regard to percolation, i.e.pc>p> 1 –pc.Furthermore, we show that asp↑pcorp↓ (1 –pc), the interface density vanishes with scaling behavior identical to the correlation length of the site percolation problem.
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47

Chayes, L., and C. Winfield. "The density of interfaces: a new first-passage problem." Journal of Applied Probability 30, no. 4 (December 1993): 851–62. http://dx.doi.org/10.2307/3214517.

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We introduce and study a novel type of first-passage percolation problem on where the associated first-passage time measures the density of interface between two types of sites. If the types, designated + and –, are independently assigned their values with probability p and (1 — p) respectively, we show that the density of interface is non-zero provided that both species are subcritical with regard to percolation, i.e. pc > p > 1 – pc. Furthermore, we show that as p ↑ pc or p ↓ (1 – pc), the interface density vanishes with scaling behavior identical to the correlation length of the site percolation problem.
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48

Howard, C. Douglas. "Differentiability and monotonicity of expected passage time in Euclidean first-passage percolation." Journal of Applied Probability 38, no. 04 (December 2001): 815–27. http://dx.doi.org/10.1017/s0021900200019057.

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In first-passage percolation (FPP) models, the passage time T ℓ from the origin to the point ℓe ℓ satisfies f(ℓ) := ET ℓ = μℓ + o(ℓ ½+ε), where μ ∊ (0,∞) denotes the time constant. Yet, for lattice FPP, it is not known rigorously that f(ℓ) is eventually monotonically increasing. Here, for the Poisson-based Euclidean FPP of Howard and Newman (Prob. Theory Relat. Fields 108 (1997), 153–170), we prove an explicit formula for f′(ℓ). In all dimensions, for certain values of the model's only parameter we have f′(ℓ) ≥ C > 0 for large ℓ.
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49

Howard, C. Douglas. "Differentiability and monotonicity of expected passage time in Euclidean first-passage percolation." Journal of Applied Probability 38, no. 4 (December 2001): 815–27. http://dx.doi.org/10.1239/jap/1011994174.

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In first-passage percolation (FPP) models, the passage time Tℓ from the origin to the point ℓeℓ satisfies f(ℓ) := ETℓ = μℓ + o(ℓ½+ε), where μ ∊ (0,∞) denotes the time constant. Yet, for lattice FPP, it is not known rigorously that f(ℓ) is eventually monotonically increasing. Here, for the Poisson-based Euclidean FPP of Howard and Newman (Prob. Theory Relat. Fields108 (1997), 153–170), we prove an explicit formula for f′(ℓ). In all dimensions, for certain values of the model's only parameter we have f′(ℓ) ≥ C > 0 for large ℓ.
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50

PIMENTEL, LEANDRO P. R. "Asymptotics for First-Passage Times on Delaunay Triangulations." Combinatorics, Probability and Computing 20, no. 3 (February 3, 2011): 435–53. http://dx.doi.org/10.1017/s0963548310000477.

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In this paper we study planar first-passage percolation (FPP) models on random Delaunay triangulations. In [14], Vahidi-Asl and Wierman showed, using sub-additivity theory, that the rescaled first-passage time converges to a finite and non-negative constant μ. We show a sufficient condition to ensure that μ>0 and derive some upper bounds for fluctuations. Our proofs are based on percolation ideas and on the method of martingales with bounded increments.
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