Ramdom walks on hypergroup of circles in finite fields

Details Ramdom walks on hypergroup of circles in finite fields Ramdom walks on hypergroup of circles in finite fields

2005-08-22

arxiv.org/abs/math/0508403v1

Mathematics

Combinatorics

14 pages, to appear in Proceeding of Australasian Workshop of Combinatorics Algorithms

Scientific paper

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.

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