  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.
