Gleichverteilung auf diskreten Halbgruppen.
Green functions and spectra on free products of cyclic groups
Green functions of a stochastic operator on a free product of cyclic groups are explicitly evaluated as algebraic functions. The spectra are investigated by Morse theoretic argument.
Groupe de Stam d'une probabilité
Hardy-Littlewood theory on unimodular groups
Harmonic Analysis and Spectral Synthesis in Central Hypergroups.
Harmonic ergodicity of actions of certain discrete linear groups
Harmonic functions along Brownan balls an the Liouville property for solvable Lie groups.
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Hemigroups of probalitiy measures on a locally compact group.
Homomorphisms to constructed from random walks
We give a construction of homomorphisms from a group into the reals using random walks on the group. The construction is an alternative to an earlier construction that works in more general situations. Applications include an estimate on the drift of random walks on groups of subexponential growth admitting no nontrivial homomorphism to the integers and inequalities between the asymptotic drift and the asymptotic entropy. Some of the entropy estimates obtained have applications independent of the...
Horocyclic products of trees
Let be homogeneous trees with degrees , respectively. For each tree, let be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of is the graph consisting of all -tuples with , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If and then we obtain a Cayley graph of the...
How a centred random walk on the affine group goes to infinity
Ind-additive functionals on random vectors [Book]
Interlaced processes on the circle
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...
Iterates of a convolution on a non abelian group
Jacobi radial stable processes
Jucys-Murphy element and walks on modified Young graph
Biane found out that irreducible decomposition of some representations of the symmetric group admits concentration at specific isotypic components in an appropriate large n scaling limit. This deepened the result on the limit shape of Young diagrams due to Vershik-Kerov and Logan-Shepp in a wider framework. In particular, it is remarkable that asymptotic behavior of the Littlewood-Richardson coefficients in this regime was characterized in terms of an operation in free probability of Voiculescu....
Krengel-Lin decomposition for noncompact groups
La loi du logarithme itéré bornée dans les espaces de Banach
Large-scale isoperimetry on locally compact groups and applications
We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first...