Collisions of random walks in dynamic random environments

被引：2

作者：

Halberstam, Noah ^{[1
]}

Hutchcroft, Tom ^{[2
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge, England

[2] CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2022年 / 27卷

关键词：

random walks; collisions; dynamical percolation; dynamic random environments; INDEPENDENT RANDOM-WALKS; INVARIANCE-PRINCIPLE; TIME;

D O I：

10.1214/21-EJP738

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study dynamic random conductance models on Z2 in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally independent random walks in the same environment collide infinitely often almost surely. These results apply in particular to random walks on dynamical percolation.

引用

页数：18

共 42 条

[1] Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights [J].

Andres, Sebastian ;

Chiarini, Alberto ;

Slowik, Martin .

PROBABILITY THEORY AND RELATED FIELDS, 2021, 179 (3-4) :1145-1181

[2]

Andres S, 2021, J STAT PHYS, V182, DOI 10.1007/s10955-021-02705-5

[3] Green kernel asymptotics for two-dimensional random walks under random conductances [J].

Andres, Sebastian ;

Deuschel, Jean-Dominique ;

Slowik, Martin .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25 :1-14

[4] QUENCHED INVARIANCE PRINCIPLE FOR RANDOM WALKS WITH TIME-DEPENDENT ERGODIC DEGENERATE WEIGHTS [J].

Andres, Sebastian ;

Chiarini, Alberto ;

Deuschel, Jean-Dominique ;

Slowik, Martin .

ANNALS OF PROBABILITY, 2018, 46 (01) :302-336

[5] Invariance principle for the random conductance model with dynamic bounded conductances [J].

Andres, Sebastian .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (02) :352-374

[6]

[Anonymous], Reversible markov chains and random walks on graphs

[7] Analysis of random walks in dynamic random environments via L2-perturbations [J].

Avena, L. ;

Blondel, O. ;

Faggionato, A. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (10) :3490-3530

[8] A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model [J].

Avena, Luca ;

Blondel, Oriane ;

Faggionato, Alessandra .

JOURNAL OF STATISTICAL PHYSICS, 2016, 165 (01) :1-23

[9] Symmetric exclusion as a model of non-elliptic dynamical random conductances [J].

Avena, Luca .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2012, 17 :1-8

[10]

Ball Keith, 1992, Geom. Funct. Anal, P137

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