A Model for Random Random-Walks on Finite Groups
- 1 March 1997
- journal article
- research article
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 6 (1) , 49-56
- https://doi.org/10.1017/s096354839600257x
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 k − d → ∞ almost all of the random-walks converge to uniform in k ln (k/(k − d))/4+ρk steps, where ρ is any constant satisfying ρ > −ln (ln 2)/4.Keywords
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