1,016 research outputs found
Asymptotic behavior of convolution powers of a probability measure on harmonic extensions of H groups
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Spectral analysis of finite Markov chains with spherical symmetries
No full textWe generalize the classical Fourier analysis of Gelfand pairs to the setting of groups acting not transitively on a set X. We use this analysis to determine the spectrum of several random walks on graphs. Moreover, as byproduct, we show that, for a new urn diffusion model, the cut-off phenomenon holds
Harmonic analysis of finite lamplighter random walks
No full textRecently, several papers have been devoted to the analysis of lamplighter random walks, in particular, in the case where the underlying graph is the infinite path Z. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C-2-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. If the graph has a transitive isometry group G, we also describe the spectral analysis in terms of the representation theory of the wreath product C-2 (sic) G. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples have already been studied by Haggstrom and Jonasson by probabilistic methods
Induced representations and harmonic analysis on finite groups
No full textThe aim of the present paper is to develop a theory of spherical functions for noncommutative Hecke algebras on finite groups. Let G be a finite group, K a subgroup and (Î ̧, V) an irreducible, unitary K-representation. After a careful analysis of Frobenius reciprocity, we are able to introduce an orthogonal basis in the commutant of IndKGV, and an associated Fourier transform. Then we translate our results in the corresponding Hecke algebra, an isomorphic algebra in the group algebra of G. Again a complete Fourier analysis is developed. As particular cases, we obtain some classical results of Curtis and Fossum on the irreducible characters. Finally, we develop a theory of GelfandâTsetlin bases for Hecke algebras
Harmonic analysis on a finite homogeneous space II: the Gelfand Tsetlin decomposition
No full textIn this paper, we continue the analysis of [28] on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. We extend the theory of Gelfand-Tsetlin bases to permutation representations. Then we study several concrete examples on the symmetric groups, generalizing the Gelfand pair of the Johnson scheme. We also extend part of the Okounkov-Vershik theory to the Young permutation module M-a. In particular we constuct explicit Gelfand-Tsetlin bases for the representation S-n-1,S-1. We also give an explicit Gelfand-Tsetlin decomposition for the permutation module associated with a three-parts partitions, using James reformulation of the Young rule by means of intertwining operators (Radon transforms). Several statistical applications, refining previous work by Diaconis, are given. Finally, the spectrum of several invariant operators is determined
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