Hypergroups associated to random walks on the Platonic solids
نویسنده
چکیده
We explicitly construct the convolution hypergroups of spheres in the vertex graphs of the classical Platonic solids, their character tables, and the structure of their dual signed hypergroups. This allows us to easily determine certain aspects of the random walks on these graphs. The character tables share many of the pleasant properties of character tables of finite groups.
منابع مشابه
Bessel 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 کاملRandom walks on hypergroup of conics in finite fields
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,...
متن کاملEdgeworth Expansion on N{spheres and Jacobi Hypergroups
Suitable normalization of time{homogeneous rotation{invariant random walks on unit spheres S d R d+1 for d > 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is diierent from the classical case. The proof is performed in the more general setting o...
متن کاملConstructing Finite Frames via Platonic Solids
Finite tight frames have many applications and some interesting physical interpretations. One of the important subjects in this area is the ways for constructing such frames. In this article we give a concrete method for constructing finite normalized frames using Platonic solids.
متن کاملAnalysis on Symmetric Cones (oxford Mathematical Monographs)
measure always exists on a commutative hypergroup K, and there always exists a 'Plancherel measure' on the dual space K of equivalence classes of irreducible representations of K, with respect to which Plancherel's formula holds for Fourier transforms. In contrast with the case of a locally compact abelian group, however, the Plancherel measure is not necessarily a Haar measure on K, and K need...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004