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arXiv · 1310.6781

Quantitative equidistribution for certain quadruples in quasi-random groups

Tim Austin
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Abstract

In a recent paper (arXiv:1211.6372), Bergelson and Tao 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 notes gives a rather more elementary proof which improves this to an explicit polynomial bound in $D^{-1}$.

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Tim Austin. 2015-07-08. Quantitative equidistribution for certain quadruples in quasi-random groups. https://doi.org/10.1017/s0963548314000492

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