Mixability of finite groups

We say that a finite group G is mixable if there exists a sequence of independent random choices, each between two fixed group elements, whose product is uniformly distributed on G. This notion originates in work of Angel and Holroyd studying such mixings of the symmetric groups via lazy transpositions. In this talk, we will discuss properties of mixable groups and present conditions and obstructions to mixability. We will explore mixability in various families of groups including p-groups, permutation groups, matrix groups, Coxeter groups, and certain sporadic simple groups. We will also discuss bounds on the minimal length of a sequence required to achieve uniformity.

 

Based on joint work with Gideon Amir, Subhajit Ghosh and Uzi Vishne.