Related papers: A L\'evy-Khinchin formula for free groups

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not. Given a finitely generated subgroup G of a finite product of limit groups, we…

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions,…

In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and…

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.

We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\'evy constant…

For L\'evy processes with matrix-exponential negative jumps, the unified form of the Pollaczek-Khinchine formula is established.

There are given sufficient conditions under which mixtures of dilations of L\'evy spectral measures, on a Hilbert space, are L\'evy measures again. We introduce some random integrals with respect to infinite dimensional L\'evy processes,…

Positive definite functions are fundamental to many areas of applied mathematics, probability theory, spatial statistics and machine learning, amogst others. Motivated by a problem coming from the maximum likelihood estimation under fixed…

The residual finiteness growth $\text{RF}_G: \mathbb{N} \to \mathbb{N}$ of a finitely generated group $G$ is a function that gives the smallest value of the index $[G:N]$ with $N$ a normal subgroup not containing a non-trivial element $g$,…

We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the independence number of the defining graph. We also make a…

The new model for the free solvable groups of level two is given; this helps to calculate the Poisson-Furstenberg boundary of the group.

This paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved…

We calculate explicitly the normal zeta function of the free class two nilpotent group on four generators. This has Hirsch length ten.

We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…

We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit…

In this paper, the author (1) compares subnormal closures of finite sets in free groups; (2) proves that the exponential growth rate (e.g.r.), i.e., the limit of the n-th roots of g(n), where g(n) is the growth function of a subgroup H with…

Given a finitely generated residually finite group $G$, the residual finiteness growth $\text{RF}_G: \mathbb{N} \to \mathbb{N}$ bounds the size of a finite group $Q$ needed to detect an element of norm at most $r$. More specifically, if…

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the $L^2$-operator norm of the maximal function associated to a kernel $K\in L^1,$ with differentiable…

There are many "minimax" complexity functions in mathematics: width of a tree or a link, Heegaard genus of a 3-manifold, the Cheeger constant of a Riemannian manifold. We define such a function w, "width", on countable (or finite) groups…

In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual…