Date of Award
8-2016
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
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.
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