Related papers: Free Infinite Divisibility for Q-Gaussians

We produce new examples of totally imaginary infinite extensions of $\mathbb{Q}$ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for $\mathbb{Q}^{(2)}$. In particular, we use…

The notion of a $*$-law or $*$-distribution in free probability is also known as the quantifier-free type in Farah, Hart, and Sherman's model theoretic framework for tracial von Neumann algebras. However, the full type can also be…

We study two dimensional massless field in a box with potential $V\left( \nabla \phi \left( \cdot \right) \right) $ and zero boundary condition, where $V$ is any symmetric and uniformly convex function. Naddaf-Spencer and Miller proved the…

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…

This paper addresses two of Kaplansky's conjectures concerning group rings $K[G]$, where $K$ is a field and $G$ is a torsion-free group: the zero-divisor conjecture, which asserts that $K[G]$ has no non-trivial zero-divisors, and the unit…

We give a streamlined proof of the limit theorems for the free additive convolution of infinitesimal triangular arrays of probability measures on the real line. The result was first proved by Chistyakov and G\"otze using analytic…

The q-Gaussian function emerges naturally in various applications of statistical mechanics of non-ergodic and complex systems. In particular it was shown that in the theory of binary processes with correlations, the q-Gaussian can appear as…

A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-dynamical system corresponding to these expansions. Then,…

Let $k$ be a field of characteristic different from $2$ and let $G$ be a nonabelian residually torsion-free nilpotent group. It is known that $G$ is an orderable group. Let $k(G)$ denote the subdivision ring of the Malcev-Neumann series…

In this paper, we consider a variant of Tur\'an's problem on the distance from an integer polynomial in $\mathbb{Z}[x]$ to the nea\-rest irreducible polynomial in $\mathbb{Z}[x]$. We prove that for any polynomial $f \in \mathbb{Z}[x]$,…

In 1971 Cusick proved that every real number $x\in[0,1]$ can be expressed as a sum of two continued fractions with no partial quotients equal to $1$. In other words, if we define a set $$ S(k):= \{ x\in[0,1] : a_n(x) \geq k \text{ for all }…

Let $B$ be a finite, separable von Neumann algebra. We prove that a $B$-valued distribution $\mu$ that is the weak limit of an infinitesimal array is infinitely divisible. The proof of this theorem utilizes the Steinitz lemma and may be…

A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…

An algebraic approach is developed to define and study infinite dimensional grassmannians. Using this approach a quantum deformation is obtained for both the ind-variety union of all finite dimensional grassmannians, and the Sato…

A finite group $G$ is called $\psi$-divisible if $\psi(H)|\psi(G)$ for any subgroup $H$ of $G$, where $\psi(H)$ and $\psi(G)$ are the sum of element orders of $H$ and $G$, respectively. In this paper, we extend a result provided in [10], by…

The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q,t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish…

We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method is very flexible and can also be used to study (partially) periodic quotients of any group which admits an action on a hyperbolic…

In this paper, we are interested in a generalization of the notion of sum-free sets. We address a conjecture first made in the 90s by Chung and Goldwasser. Recently, after some computer checks, this conjecture was formulated again by…

We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or p-adic field are infinitely…

We construct a random matrix model for the bijection \Psi between clas- sical and free infinitely divisible distributions: for every d\geq1, we associate in a quite natural way to each *-infinitely divisible distribution \mu a distribution…