Related papers: Free Infinite Divisibility for Q-Gaussians

In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs…

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…

Let $\mathbb{F}_q$ denote the finite field of $q$ elements with characteristic $p$. Let $\mathbb{Z}_q$ denote the unramified extension of the $p$-adic integers $\mathbb{Z}_p$ with residue field $\mathbb{F}_q$. In this paper, we investigate…

We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to…

In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our results include infinitely divisible measures with respect to…

The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and…

We prove that the phase transition for the Gaussian free field (GFF) is sharp. In comparison to a previous argument due to Rodriguez in 2017 which characterized a $0-1$ law for the Massive Gaussian Free Field by analyzing crossing…

We consider a family of continued fraction expansions of any number in the unit closed interval $[0,1]$ whose digits are differences of consecutive non-positive integer powers of an integer $m \geq 2$. For this expansion, we apply the…

This paper establishes the theoretical foundations for the asymptotic separability of Gaussian Mixture Models (GMMs) in high dimensions by extending the classical Feldman-H\'ajek theorem. We first prove that a countable mixture of Gaussian…

In this work, we explore both the ordinary $q$-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the $q$-deformed diffusion differential equation. This…

An infinite family of irreducible homogeneous free divisors in $K[x, y, z]$ is constructed. Indeed, we identify sets of monomials $X$ such that the general polynomial supported on $X$ is a free divisor.

Quasi-infinitely divisible (QID) distributions have been recently introduced by Lindner, Pan and Sato (\textit{Trans.~Amer.~Math.~Soc.}~\textbf{370}, 8483-8520 (2018)). A random variable $X$ is QID if and only if there exist two infinitely…

This paper investigates the periodic points of the Gauss type shifts associated to the even continued fraction (Schweiger) and to the backward continued fraction (R\'enyi). We show that they coincide exactly with two sets of quadratic…

According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show that this indeed is the case with conditional density…

Every integer greater than two can be expressed as the sum of a prime and a square-free number. Expanding on recent work, we provide explicit and asymptotic results when divisibility conditions are imposed on the square-free number. For…

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as…

Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient…

For a real Hilbert space $H_{\mathbb{R}}$ and $-1 < q < 1$ Bozejko and Speicher introduced the C$^\ast$-algebra $A_q(H_{\mathbb{R}})$ and von Neumann algebra $M_q(H_{\mathbb{R}})$ of $q$-Gaussian variables. We prove that if…

Let $k$ be a division ring and let $G$ be either a torsion-free virtually compact special group or a finitely generated torsion-free $3$-manifold group. We embed the group algebra $kG$ in a division ring and prove that the embedding is…

Let $\mu$ be a probability measure on the real line. In this paper we prove that there exists a decomposition $\mu = \mu_{0} \boxplus \mu_{1} \boxplus \... \boxplus \mu_{n} \boxplus \...$ such that $\mu_{0}$ is infinitely divisible and…