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A non-local random walk on the hypercube

Published online by Cambridge University Press:  17 November 2017

Evita Nestoridi*
Affiliation:
Stanford University
*
* Current address: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA. Email address: [email protected]

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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