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Group representations that resist random sampling
Published Web Location
https://arxiv.org/pdf/1405.3636.pdfNo data is associated with this publication.
Abstract
We 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.
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