Publisher： John Wiley & Sons Inc
E-ISSN： 1098-2418|47|3|605-614
ISSN： 1042-9832
Source： RANDOM STRUCTURES AND ALGORITHMS, Vol.47, Iss.3, 2015-10, pp. : 605-614
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Abstract
AbstractWe show that there exists a family of groups Gn and nontrivial irreducible representations ρn such that, for any constant t, the average of ρn over t uniformly random elements g1,…,gt∈Gn has operator norm 1 with probability approaching 1 as n→∞. More quantitatively, we show that there exist families of finite groups for which Ω(loglog|G|) random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 605–614, 2015
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