Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 $D^{-1}$.
['Tim Austin']
I am writing a research paper on a idea Quantitative equidistribution for certain quadruples in quasi-random groups
[{"from": "human", "value": "I am writing a research paper on a idea Quantitative equidistribution for certain quadruples in quasi-random groups"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 $D^{-1}$."}]