# Ramdom walks on hypergroup of circles in finite fields

Research paper by Le Anh Vinh

Indexed on: 22 Aug '05Published on: 22 Aug '05Published in: Mathematics - Combinatorics

#### Abstract

In this paper we study random walks on the hypergroup of circles in a finite field of prime order p = 4l + 3. We investigating the behavior of random walks on this hypergroup, the equilibrium distribution and the mixing times. We use two different approaches - comparision of Dirichlet forms (geometric bound of eigenvalues), and coupling methods, to show that the mixing time of random walks on hypergroup of circles is only linear.