Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T17:25:29.436Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups

Published online by Cambridge University Press:  02 October 2014

TIM AUSTIN
TIM AUSTIN*
Affiliation:
Courant Institute, New York University, New York, NY 10012, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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 G4 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.

Keywords

Primary 05D99Secondary 20C1537A25
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 2 , March 2015 , pp. 376 - 381
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bergelson, V. and McCutcheon, R. (2007) Central sets and a non-commutative Roth theorem. Amer. J. Math. 129 1251–1275.CrossRefGoogle Scholar
[2]Bergelson, V. and Tao, T. (2014) Multiple recurrence and quasirandom groups. Geom. Funct. Anal. 24 1–48.Google Scholar
[3]Bump, D. (2004) Lie Groups, Vol. 225 of Graduate Texts in Mathematics, Springer.Google Scholar
[4]Furstenberg, H. (1977) Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math. 31 204–256.Google Scholar
[5]Gowers, W. T. (2008) Quasirandom groups. Combin. Probab. Comput. 17 363–387.Google Scholar
[6]Tserunyan, A. Mixing and triple recurrence in probability groups. Preprint. arXiv.org:1405.5629Google Scholar