[HTML][HTML] Studies on the Marchenko–Pastur Law
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 …
introduced. This theory is about a set of probability measures defined using the Cauchy …
[HTML][HTML] Some Results on the Free Poisson Distribution
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 …
nondegenerate probability measures μ 1 and μ 2 with support bounded from above. Define …
Free quantitative fourth moment theorems on Wigner space
S Bourguin, S Campese - International Mathematics Research …, 2018 - academic.oup.com
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 …
symmetric kernels, generalizing an earlier result from Kemp et al.(2012). The proof relies on …
Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle
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 …
and of universal limit theorems, for multilinear homogeneous sums, in both the classical and …
A four moments theorem for gamma limits on a Poisson chaos
T Fissler, C Thäle - arXiv preprint arXiv:1502.01568, 2015 - arxiv.org
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 …
q $ generated by a Poisson random measure on a Polish space. The problem is …
Universality and Fourth Moment Theorem for homogeneous sums. Orthogonal polynomials and apolarity
R Simone - arXiv preprint arXiv:1705.03294, 2017 - arxiv.org
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 …
Moment Theorem and universality properties for homogeneous sums, while the last part …
[PDF][PDF] Universality and Fourth Moment Theorem for homogeneous sums. Orthogonal polynomials and apolarity
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 …
Fourth Moment Theorem and the universality phenomenon in the framework of …
Multidimensional Free Poisson Limits on Free Stochastic Integral Algebras
M Gao, J Fang - arXiv preprint arXiv:1706.09198, 2017 - arxiv.org
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 …
free Wigner chaos or the free Poisson algebra. We prove that, under mild technical …
Freeness characterizations on free chaos spaces
S Bourguin, I Nourdin - Pacific Journal of Mathematics, 2020 - msp.org
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 …
with respect to a free Brownian motion or a free Poisson process. We obtain three …
Multidimensional limit theorems for homogeneous sums: a general transfer principle
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 …
{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic …