
TL;DR
This paper investigates the cutoff phenomenon and mixing times of random walks on cyclic groups with uniform symmetric generators, providing insights into the transition to stationarity in these Markov chains.
Contribution
It analyzes the cutoff phenomenon for random walks on cyclic groups with uniform symmetric generators, extending understanding of mixing times in these settings.
Findings
Identifies conditions under which cutoff occurs
Provides bounds on mixing times for specific generating sets
Enhances understanding of phase transition in Markov chains
Abstract
Given a sequence of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and the cut-off phenomenon in the total variation metric in the case of random walk on the groups , prime, with driving measure uniform on a symmetric generating set .
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