Efficient Coupling for Random Walk with Redistribution

Authors

Elizabeth TrippFollow

Date of Completion

Spring 5-1-2015

Thesis Advisor(s)

Iddo Ben-Ari

Honors Major

Mathematics

Disciplines

Other Mathematics

Abstract

What can be said on the convergence to stationarity of a finite state Markov chain that behaves 'locally' like a nearest-neighbor random walk on the set of integers? In this work, we looked to obtain sharp bounds for the rate of convergence to stationarity for a particular non-symmetric Markov chain. Our Markov chain is a variant of the simple symmetric random walk on the state space {0, ..., N} obtained by allowing transitions from 0 to J₀ and from N to J_N. We first looked at the case where J₀ and J_N are fixed, deterministic sites; we then also considered the case where J₀ and J_N are repeatedly sampled from some given probability distribution. For each of these two cases, we constructed an efficient coupling for the model, giving an intuitive and probabilistic explanation for the rates of convergence as well as providing sharp, computable, and non-asymptotic bounds.

Recommended Citation

Tripp, Elizabeth, "Efficient Coupling for Random Walk with Redistribution" (2015). Honors Scholar Theses. 458.
https://digitalcommons.lib.uconn.edu/srhonors_theses/458