In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been
introduced. This theory is about a set of probability measures defined using the Cauchy …

Let K+(μ i)={Q si μ i, si∈(m 0 μ i, m+ μ i)}, i= 1, 2, be two CSK families generated by the
nondegenerate probability measures μ 1 and μ 2 with support bounded from above. Define …

We prove a quantitative fourth moment theorem for Wigner integrals of any order with
symmetric kernels, generalizing an earlier result from Kemp et al.(2012). The proof relies on …

We provide a synthetic yet comprehensive review of the so-called fourth moment criterion,
and of universal limit theorems, for multilinear homogeneous sums, in both the classical and …

This paper deals with sequences of random variables belonging to a fixed chaos of order $
q $ generated by a Poisson random measure on a Polish space. The problem is …

The aim of the dissertation is threefold: the first two parts are devoted to explore the Fourth
Moment Theorem and universality properties for homogeneous sums, while the last part …

The aim of the present essay is threefold: the first two parts are devoted to fully explore the
Fourth Moment Theorem and the universality phenomenon in the framework of …

In this paper, we prove four-moment theorems for multidimensional free Poisson limits on
free Wigner chaos or the free Poisson algebra. We prove that, under mild technical …

We deal with characterizing the freeness and asymptotic freeness of free multiple integrals
with respect to a free Brownian motion or a free Poisson process. We obtain three …

The aim of the present paper is to establish the multidimensional counterpart of the\textit
{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic …