Random walks on hypergroup of conics in finite fields
نویسنده
چکیده
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, finite fields.
منابع مشابه
Random walks on the hypergroup of circles in a finite field
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...
متن کاملHypergroups derived from random walks on some infinite graphs
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.
متن کاملSU(d)-biinvariant random walks on SL(d,C) and their Euclidean counterparts
Motivated by recent results of A. Klyachko, we construct a probability preserving, isometric isomorphism from the Banach algebra Mb(SL(d,C)‖SU(d)) of all SU(d)-biinvariant bounded signed measures on SL(d,C) to some Banach subalgebra of the Banach algebra of all bounded signed measures on the Euclidean space of all Hermitian d × d-matrices with trace 0. This isomorphism leads to strong limit the...
متن کاملBessel convolutions on matrix cones: Algebraic properties and random walks
Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite q×q-matrices over R,C,H were introduced recently by Rösler. These convolutions depend on some continuous parameter, generate commutative hypergroup structures and have Bessel functions of matrix argument as characters. Here, we first study the rich algebraic structure of these hypergroups. In...
متن کاملGroup Representations and High-Resolution Central Limit Theorems for Subordinated Spherical Random Fields
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we establish a new connection with random walks on the hypergroup ŜO (3) (the dual of SO (3)), which mirrors analogous results previously established for fields de...
متن کامل