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Maxima of entries of Haar distributed matrices
Let Γ n =( γ ij ) be an n × n random matrix such that its distribution is the normalized Haar measure on the orthogonal group O ( n ). Let also W ...
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Cumulants are universal homomorphisms into Hausdorff groups
This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob
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Isotropic random walks in a building of type
Let d ≥1 be an integer, and let
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Liouville property for groups and manifolds
We introduce a method to estimate the entropy of random walks on groups. We apply this method to exhibit the existence of compact manifolds with...
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A characterization of the Gaussian distribution on Abelian groups
It is well known that the independence of two linear forms with nonzero coefficients of independent random variables implies that the random...
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Some dichotomy results for central Gaussian convolution semigroups on compact groups
Consider a central Gaussian convolution semigroup (μ t ) t > 0 on a connected compact semisimple group. Then either the measure μ t is singular with...
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Group extensions of Gibbs–Markov maps
Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group ? defined on an exact Gibbs–Markov map T : X → X . We...
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Eigenvalue distributions of random unitary matrices
Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of...
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Growth Series and Random Walks on Some Hyperbolic Graphs
Consider the tessellation of the hyperbolic plane by m -gons, ℓ per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics,...
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On a Class of Non-Translation Invariant Feller Semigroups on Lie Groups
We consider a class of Feller semigroups on Lie groups which fail to commute with left translation due to the existence of a cocycle h which is...
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Hilbert Spaces Induced by Toeplitz Covariance Kernels
We consider the reproducing kernel Hilbert space H μ induced by a kernel which is obtained using the Fourier-Stieltjes transform...
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Kerov’s Central Limit Theorem for the Plancherel Measure on Young Diagrams
Consider random Young diagrams with fixed number n of boxes, distributed according to the Plancherel measure M n. That is, the weight...
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A Local Limit Theorem on Certain p-AdicGroups and Buildings
We present a local limit theorem for a measure on the special linear group with entries in a local field.
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Recent results on functional equations in a single variable, perspectives and open problems
In 1990 Cambridge University Press published the by now well-known monograph Iterative Functional Equations by Marek Kuczma, Bogdan Choczewski and...
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Unimodality of Stable Gaussian Laws on the Heisenberg Group
We prove unimodality of all dilatation-stable Gaussian laws on the Heisenberg group.
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A central limit theorem for exchangeable random variables on a locally compact abelian group
A central limit theorem is given for uniformly infinitesimal triangular arrays of random variables in which the random variables in each row are...
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On Diffusion Hemigroups of Probability Measures on an Abelian Locally Compact Group
The connections are investigated between the diffusion property for a two-parameter semigroup (hemigroup) of probability measures on an abelian...
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Strongly τ-Decomposable and Selfdecomposable Laws on Simply Connected Nilpotent Lie Groups
Let ? be a simply connected nilpotent Lie group with Lie Algebra ? and let τ be a contraction on ?. A probability measure μ on ? is strongly...
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Lindeberg-Feller theorems on Lie groups
Necessary and sufficient conditions are given for a triangular array of probability measures on an arbitrary Lie group to converge to a Gauss...