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A Model for Random Random-Walks on Finite Groups

Published online by Cambridge University Press:  01 March 1997

ANDREW S. GREENHALGH
Affiliation:
Department of Mathematics, The Catholic University of America, Washington, DC 20064, USA

Abstract

A model for a random random-walk on a finite group is developed where the group elements that generate the random-walk are chosen uniformly and with replacement from the group. When the group is the d-cube Zd2, it is shown that if the generating set is size k then as d → ∞ with kd → ∞ almost all of the random-walks converge to uniform in k ln (k/(kd))/4+ρk steps, where ρ is any constant satisfying ρ > −ln (ln 2)/4.

Type
Research Article
Copyright
1997 Cambridge University Press

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