Related papers: Locally Random Groups
The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…
We present an algorithm for the determination of the local symmetry group for arbitrary k-points in 3D Brillouin zones. First, we test our implementation against tabulated results available for standard high-symmetry points (given by…
It has been shown in a recent work by Yakir-Zeitouni that the minimum modulus of random trigonometric polynomials with Gaussian coefficients has a limiting exponential distribution. We show this is a universal phenomenon. Our approach…
Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As is common in probability theory, it would be desirable to…
In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of…
In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a…
This is an expostion of various aspects of amenability and paradoxical decompositions for groups, group actions and metric spaces. First, we review the formalism of pseudogroups, which is well adapted to stating the alternative of Tarski,…
We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven…
We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the associated harmonic measure, a key element in formulating…
We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain an explicit spectral decomposition of the local descents at the first occurrence index in terms of the local…
Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix…
This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $\nu$ associated with such a random walk. We first establish a link of the form $\dim \nu \leq…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…
We introduce a notion of covolume for point sets in locally compact groups that simultaneously generalizes the covolume of a lattice and the reciprocal of the Beurling density for amenable, unimodular groups. This notion of covolume arises…
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…