Related papers: Free Infinite Divisibility for Ultrasphericals

We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.

It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges. We prove a limit law…

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their…

Let $M$ be a finite volume hyperbolic manifold, we show the equidistribution in $M$ of the equidistant hypersurfaces to a finite volume totally geodesic submanifold $C$. We prove a precise asymptotic on the number of geodesic arcs of…

We establish a class of sufficient conditions, ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this result to construct a set of explicit counterexamples,…

We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cubulated group has a cubulation for which all halfspaces are…

We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in…

Motivated by questions of Fouvry and Rudnick on the distribution of Gaussian primes, we develop a very general setting in which one can study inequities in the distribution of analogues of primes through analytic properties of infinitely…

We prove that every non-finitely generated projective module over the integral group ring of a polycyclic-by-finite group G is free if and only if G is polycyclic.

Free products of two residually finite groups with amalgamated retracts are considered. It is proved that a cyclic subgroup of such a group is not finitely separable if, and only if, it is conjugated with a subgroup of a free factor which…

We study two ways (levels) of finding free-probability analogues of classical infinitely divisible measures. More precisely, we identify their Voiculescu transforms. For free-selfdecomposable measures we found the formula (a differential…

We show that in any infinitely distributive inverse semigroup the existing binary meets distribute over all the joins that exist.

We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.

Several quantities related to the Zernike circle polynomials admit an expression as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the…

We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The…

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued…