A Berry-Esseen theorem on semisimple Lie groups
A Central Limit Theorem for Approximate Martingale Arrays with Values in a Locally Compact Abelian Group.
A central limit theorem on the space of positive definite symmetric matrices
A central limit theorem is proved on the space of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on are defined and investigated. One uses a Taylor expansion of the spherical functions on .
A Decomposition Theorem for Additive Set-Functions, with Applications to Pettis Integrals and Ergodic Means.
A Gaussian bound for convolutions of functions on locally compact groups
We give new and general sufficient conditions for a Gaussian upper bound on the convolutions of a suitable sequence K₁, K₂, K₃, ... of complex-valued functions on a unimodular, compactly generated locally compact group. As applications, we obtain Gaussian bounds for convolutions of suitable probability densities, and for convolutions of small perturbations of densities.
A general Choquet–Deny theorem for nilpotent groups
A general purity law for convolution semigroups with discrete Levy measure.
A Green's Function for Non-Homogegeous Random Walks on Free Products.
A Law of the Iterated Logarithm for a Class of Polynomial Hypergroups.
A Littlewood-Paley-Stein estimate on graphs and groups
We establish the boundedness in spaces, 1 < q ≤ 2, of a “vertical” Littlewood-Paley-Stein operator associated with a reversible random walk on a graph. This result extends to certain non-reversible random walks, including centered random walks on any finitely generated discrete group.
A Local Limit Theorem on the Semi-Direct Product of and
A New Proof of the Generalized Continuity Theorem of Paul Levy.
A remark on the norm of a random walk on surface groups
We show that the norm of the random walk operator on the Cayley graph of the surface group in the standard presentation is bounded by 1/√g where g is the genus of the surface.
A survey of results on random random walks on finite groups.
A topological version of some ergodic theorems
Absolute Continuity, Singularity, and Supports of Gauss Semigroups on a Lie Group.
Absolut-Stetigkeit und Träger von Gauß-Verteilungen auf lokalkompakten Gruppen.
Actions of large semigroups and random walks on isometric extensions of boundaries
Additive functions and singular measures
Admissible transformations of measures.