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

In this paper we study random walks on the hypergroup of conics in finite fields. We investigate the behavior of random walks on this hypergroup, the equilibrium distribution and the mixing times. We use the coupling method to show that the mixing time of random walks on hypergroup of conics is only linear. Mathematics Subject Classifications: 60D05, 11A99. Keywoords: random walks, hypergroups,...

Our interest in this paper is to define and study the concept of a fuzzy hypergroup, which depends on the concept of a fuzzy space. Indeed, the paper is a continuation of ideas presented by Davvaz [Fuzzy Sets and Systems, 101 (1999) 191-195]. A relation between a fuzzy hypergroup based on a fuzzy space and a fuzzy hypergroup in the sense of Davvaz is obtained 2010 AMS Classification: 20N20

This paper is the results of the ideas suggested by P. Corsini in his paper [10]. Our investigations take in account the paper [13] of I. Cristea. We study the hypergroup generated by the cosets modulo a subgroup (normal subgroup). We prove that (G/H, ◦4) is a complete hypergroup. We take many particular examples to illustrate some known results on hypergroups. Keyword: fuzzy sets, hypergroups,...

This paper investigates the question of when a finite hypergroup with three elements is strong, that is satisfies the condition that its dual signed hypergroup is actually a hypergroup. We classify hermitian hypergroups of order three by weight into two dimensional families and show that the algebraic conditions arising from duality yield four interesting curves in the plane which bound the cha...

A homomorphism of a hypergroup (H, ◦) is a function f : H → H satisfying f(x ◦ y) ⊆ f(x) ◦ f(y) for all x, y ∈ H. A homomorphism of a hypergroup (H, ◦) is called an epimorphism if f(H) = H. Denote by Hom(H, ◦) and Epi(H, ◦) the set of all homomorphisms and the set of all epimorphisms of a hypergroup (H, ◦), respectively. In this paper, the elements of Hom(Zn, ◦m) and Epi(Zn, ◦m) are characteriz...

This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of ‘maximal actions’ to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Followi...

Let G be a locally compact hypergroup and let K sub-hypergroup of G. (G, K) is Gelfand pair if Mc(G//K), the algebra measures with support on double coset G//K, commutative for convolution. In this paper, assuming that pair, we define study Fourier transform then establish Plancherel theorem K).

Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of finite graphs. In this article, we reveal that his method is applicable to a random walk on a certain kind of infinite graphs. Moreover, we make some observations of finite or infinite graphs on which a random walk produces a hermitian discrete hypergroup.