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A non-local random walk on the hypercube

Part of: Combinatorial probability Markov processes

Published online by Cambridge University Press:  17 November 2017

Evita Nestoridi
Evita Nestoridi*
Affiliation:
Stanford University
*
* Current address: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA. Email address: exn@princeton.edu
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Abstract

In this paper we study the random walk on the hypercube (ℤ / 2ℤ)n which at each step flips k randomly chosen coordinates. We prove that the mixing time for this walk is of the order (n / k)logn. We also prove that if k = o(n) then the walk exhibits cutoff at (n / 2k)logn with window n / 2k.

Keywords

Hypercubecouplingrandom walkEhrenfest urn model

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60C05: Combinatorial probability
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 1288 - 1299
Copyright
Copyright © Applied Probability Trust 2017 

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