Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

DOI10.1214/11-AIHP474zbMath1277.60188arXiv1011.6366MaRDI QIDQ372562

Gennady Samorodnitsky, Jonathon Peterson

Publication date: 9 October 2013

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6366

zbMATH Keywords

point processesheavy tailsweak quenched limits

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Processes in random environments (60K37) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Cites Work

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• 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
• 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
• Many visits to a single site by a transient random walk in random environment.
• Point process and partial sum convergence for weakly dependent random variables with infinite variance
• Quenched limits for the fluctuations of transient random walks in random environment on \(\mathbb{Z}\)
• Infinitely divisible random probability distributions with an application to a random motion in a random environment
• 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
• Asymptotic behaviour for random walks in random environments
• Random walks in a random environment