Convergence Rates of Random Walk on Irreducible Representations of Finite Groups

Jason Fulman ()
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Jason Fulman: University of Southern California

Journal of Theoretical Probability, 2008, vol. 21, issue 1, 193-211

Abstract: Abstract Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an asymptotic description of Plancherel measure of the finite general linear groups is given, and a connection of these random walks with the hidden subgroup problem of quantum computing is noted.

Keywords: Markov chain; Plancherel measure; Cutoff phenomenon; Finite group; Hidden subgroup problem; Quantum computing; 60C05; 20P05 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0102-1

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