Oscillation of quenched slowdown asymptotics of random walks in random environment in Z

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

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• Ahn, Sung Won

Contributors dc:contributor

• Jonathon Peterson
• Rodrigo Banuelos
• Mark Daniel Ward
• Nung Kwan Yip

• Pure sciences
• Large deviation
• Probability
• Random walk in random environment
• Mathematics

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/734

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1915