The invariance principle for group-valued random variables
The invariance principle for random variables with values in locally compact groups
The Lévy continuity theorem for nuclear groups
Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited...
The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Minlos lemma for positive-definite functions on additive subgroups of
Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let (resp. ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...
The Poisson Boundary of Polycyclic Groups
The Pólya characterization of a Gaussian measure on groups
The product-decomposability of probability measures on Abelian metrizable groups [Book]
The rate of escape for random walks on polycyclic and metabelian groups
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...
The Resolvent for Simple Random Walks on the Free Product of Two Discrete Groups.
The structure of limit measures and their supports on topological semigroups.
The Wiener Property for a Class of Discrete Hypergroups.
Théorème central limite local sur certains groupes de Lie
Théorème central limite local sur les extensions compactes de
Théorème central limite sur les groupes nilpotents
Théorème de la limite centrale pour un produit semi-direct d'un groupe de Lie résoluble simplement connexe de type rigide par un groupe compact
Théorème des grandes déviations pour les groupes de type rigide
Théorèmes limites pour les marches aléatoires sur le dual de
Transience de certaines chaînes semi-markoviennes
Transience of algebraic varieties in linear groups - applications to generic Zariski density
We study the transience of algebraic varieties in linear groups. In particular, we show that a “non elementary” random walk in escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk takes place in the real points of a semisimple split algebraic group and show such a result for a wide family of random walks.As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.