Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups
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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 .
[1] Terence Tao,et al. Multiple Recurrence in Quasirandom Groups , 2012 .
[2] Mixing and double recurrence in probability groups , 2014, 1405.5629.
[3] V. Bergelson,et al. Central sets and a non-commutative Roth theorem , 2007 .
[4] W. T. Gowers,et al. Quasirandom Groups , 2007, Combinatorics, Probability and Computing.
[5] H. Furstenberg. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions , 1977 .