Mixing and cut-off in cycle walks

Robert Hough

doi:10.1214/17-EJP108

Mixing and cut-off in cycle walks

Robert Hough

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Given a sequence (X_i, K_i)^∞i =1 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 ℤ/pℤ, p prime, with driving measure uniform on a symmetric generating set A ⊂ ℤ=pℤ.

Original language	English
Article number	90
Journal	Electronic Journal of Probability
Volume	22
DOIs	https://doi.org/10.1214/17-EJP108
State	Published - 2017

Keywords

Cut-off phenomenon
Embedded hypercube
Random lattice
Random walk on a group

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10.1214/17-EJP108

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title = "Mixing and cut-off in cycle walks",

abstract = "Given a sequence (Xi, Ki)∞i =1 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 ℤ/pℤ, p prime, with driving measure uniform on a symmetric generating set A ⊂ ℤ=pℤ.",

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AB - Given a sequence (Xi, Ki)∞i =1 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 ℤ/pℤ, p prime, with driving measure uniform on a symmetric generating set A ⊂ ℤ=pℤ.

KW - Cut-off phenomenon

KW - Embedded hypercube

KW - Random lattice

KW - Random walk on a group

UR - https://www.scopus.com/pages/publications/85032726987

U2 - 10.1214/17-EJP108

DO - 10.1214/17-EJP108

M3 - Article

SN - 1083-6489

VL - 22

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 90

ER -

Mixing and cut-off in cycle walks

Abstract

Keywords

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