Quantitative equidistribution for certain quadruples in quasi-random groups

Tim Austin

Research output: Contribution to journalArticlepeer-review


Bergelson and Tao have recently proved that if G is a D-quasi-random group, and x, g are drawn uniformly and independently from G, then the quadruple (g, x, gx, xg) is roughly equidistributed in the subset of G 4 defined by the constraint that the last two coordinates lie in the same conjugacy class. Their proof gives only a qualitative version of this result. The present note gives a rather more elementary proof which improves this to an explicit polynomial bound in D -1.

Original languageEnglish (US)
Pages (from-to)376-381
Number of pages6
JournalCombinatorics Probability and Computing
Issue number2
StatePublished - Mar 2 2015

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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