Finite Gelfand Pair Approaches for Ehrenfest Diffusion Model

Abstract

A classical diffusion model of Ehrenfest which consists of $2$-urns and $n$-balls is realized by a finite Gelfand pair $(H_n,S_n)$, where $H_n$ is the hyperoctahedral group and $S_n$ is the symmetric group. This fact can be generalized to multi-urn version by using Gelfand pairs of complex reflection groups.

7 pages