Dissertation/Thesis Abstract

Oscillation of quenched slowdown asymptotics of random walks in random environment in Z
by Ahn, Sung Won, Ph.D., Purdue University, 2016, 78; 10170588
Abstract (Summary)

We consider a one dimensional random walk in a random environment (RWRE) with a positive speed limn→∞ (Xn/) = υα > 0. Gantert and Zeitouni showed that if the environment has both positive and negative local drifts then the quenched slowdown probabilities P ω(Xn < xn) with x∈ (0,υα) decay approximately like exp{- n1-1/s} for a deterministic s > 1. More precisely, they showed that n log Pω(Xn < xn) converges to 0 or -∞ depending on whether γ > 1 - 1/s or γ < 1 - 1/ s. In this paper, we improve on this by showing that n -1+1/s log P ω(Xn < xn) oscillates between 0 and -∞ , almost surely.

Indexing (document details)
Advisor: Peterson, Jonathon
Commitee: Banuelos, Rodrigo, Ward, Mark Daniel, Yip, Nung Kwan
School: Purdue University
Department: Mathematics
School Location: United States -- Indiana
Source: DAI-B 78/03(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Large deviation, Probability, Random walk in random environment
Publication Number: 10170588
ISBN: 978-1-369-24640-7
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