Large deviations and slowdown asymptotics for one-dimensional excited random walks

Large deviations and slowdown asymptotics for one - dimensional excited random walks ∗

We study the large deviations of excited random walks on Z. We prove a large deviation principle for both the hitting times and the position of the random walk and give a qualitative description of the respective rate functions. When the excited random walk is transient with positive speed v0, then the large deviation rate function for the position of the excited random walk is zero on the inte...

Large Deviations for Random Walks in a Mixing Random Environment and Other (Non-Markov) Random Walks

We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some reinforced random walks and several classes of random walks in Gibbs fields are included. c © 2004 Wiley Periodicals, Inc.

Large Deviations and Exact Asymptotics for Constrained Exponential Random Graphs

Moderate and Small Deviations for the Ranges of One-dimensional Random Walks

We establish the moderate and small deviations for the ranges of the integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.

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

Ahn, Sung Won PhD, Purdue University, August 2016. Oscillation of Quenched Slowdown Asymptotics of Random Walks in Random Environment in Z. Major Professor: Jonathon Peterson. We consider a one dimensional random walk in a random environment (RWRE) with a positive speed limn→∞ Xn n = vα > 0. Gantert and Zeitouni [1] showed that if the environment has both positive and negative local drifts then...