### 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 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 language | English (US) |
---|---|

Pages (from-to) | 376-381 |

Number of pages | 6 |

Journal | Combinatorics Probability and Computing |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2 2015 |

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### ASJC Scopus subject areas

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

### Cite this

*Combinatorics Probability and Computing*,

*24*(2), 376-381. https://doi.org/10.1017/S0963548314000492

**Quantitative equidistribution for certain quadruples in quasi-random groups.** / Austin, Tim.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 24, no. 2, pp. 376-381. https://doi.org/10.1017/S0963548314000492

}

TY - JOUR

T1 - Quantitative equidistribution for certain quadruples in quasi-random groups

AU - Austin, Tim

PY - 2015/3/2

Y1 - 2015/3/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84921965123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921965123&partnerID=8YFLogxK

U2 - 10.1017/S0963548314000492

DO - 10.1017/S0963548314000492

M3 - Article

VL - 24

SP - 376

EP - 381

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 2

ER -