Date of Submission

Spring 2016

Academic Programs and Concentrations


Project Advisor 1

Amir Barghi

Abstract/Artist's Statement

A Markov chain is said to have a cutoff if its convergence to stationary distribution exhibits a sharp threshold. In this senior project we want to determine whether lamplighter Markov chains with prisms as underlying graphs have a cutoff. Lamplighter chains describe the stochastic process of a random walk on a graph along with the mixing of {0, 1} configurations over all vertices. A prism is defined as the Cartesian product of a cycle and a path. We provide bounds of the cover time of random walk on prisms. We run computer simulations to investigate the topic empirically. We also prove theorems about pre-cutoff, which is a weaker condition than cutoff. Finally we give the conjecture that lamplighter Markov chains on prisms have pre-cutoff but no cutoff.

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