Quenched limits for the fluctuations of transient random walks in random environment on \(\mathbb{Z}\)

DOI10.1214/12-AAP867zbMath1279.60126arXiv1012.1959MaRDI QIDQ1950266

Olivier Zindy, Nathanaël Enriquez, Christophe Sabot, Laurent Tournier

Publication date: 10 May 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1959

zbMATH Keywords

Poisson point processrandom walk in random environmentbeta distributionsfluctuation theory for random walksquenched distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Processes in random environments (60K37)

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Cites Work

• Unnamed Item
• Unnamed Item
• Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
• Quenched limit theorems for nearest neighbour random walks in 1D random environment
• Quenched limits for transient, ballistic, sub-Gaussian one-dimensional random walk in random environment
• Implicit renewal theory and tails of solutions of random equations
• Explicit stationary distributions for compositions of random functions and products of random matrices
• Limit laws for transient random walks in random environment on \(\mathbb Z\)
• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• Random difference equations and renewal theory for products of random matrices
• Quenched limits for the fluctuations of transient random walks in random environment on \(\mathbb{Z}\)
• A probabilistic representation of constants in Kesten's renewal theorem
• Simple transient random walks in one-dimensional random environment: the central limit theorem
• Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
• The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium
• Asymptotic behaviour for random walks in random environments
• Heavy-Tail Phenomena
• Extreme Values in the GI/G/1 Queue
• Probability
• Random walks in a random environment

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