Abstract
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 -γ 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.
Keywords
Pure sciences, Large deviation, Probability, Random walk in random environment
Disciplines
Mathematics
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Jonathon Peterson
Committee Chair
Jonathon Peterson
Committee Member 1
Rodrigo Banuelos
Committee Member 2
Mark Daniel Ward
Committee Member 3
Nung Kwan Yip
Date of Award
8-2016
Recommended Citation
Ahn, Sung Won, "Oscillation of quenched slowdown asymptotics of random walks in random environment in Z" (2016). Open Access Dissertations. 734.
https://docs.lib.purdue.edu/open_access_dissertations/734