activity
20102018
collaborators

9 papers

math.OA2018

-diagonal and -diagonal Pairs of Random Variables

Mingchu Gao

This paper is devoted to studying -diagonal and -diagonal pairs of random variables. We generalize circular elements to the bi-free setting, defining bi-circular element pair…

math.OA2018

Non-Gaussian Random Matrix Models for Two-faced Families of Random Variables Having Bi-free Central Limit Distributions

Mingchu Gao

In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a two-faced family of random variables having a bi-free central limit dis…

math.OA2018

Compound Bi-free Poisson Distributions

Mingchu Gao

In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distr…

math.OA2017

On Bi-free Multiplicative Convolution

Mingchu Gao

In this paper, we study the partial bi-free -transform of a pair of random variables, and the -transform of the matrix-valued random variable $\left(\begi…

math.OA2017

Multidimensional Free Poisson Limits on Free Stochastic Integral Algebras

Mingchu Gao, Junsheng Fang

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 conditio…

math.OA2016

Multidimensional Compound Poisson Distributions in Free Probability

Guimei An, Mingchu Gao

Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability,…

math.OA2015

Poisson Processes in Free Probability

Guimei An, Mingchu Gao

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free…

math.OA2015

Two-faced Families of Non-commutative Random Variables Having Bi-free Infinitely Divisible Distributions

Mingchu Gao

We study two-faced families of random variables having bi-free infinitely divisible distributions. We prove a limit theorem of the sums of bi-free two-faced pairs of random variabl…

math.OA2010

The Relative Weak Asymptotic Homomorphism Property for Inclusions of Finite von Neumann Algebras

Junsheng Fang, Mingchu Gao, Roger R. Smith

A triple of finite von Neumann algebras is said to have the relative weak asymptotic homomorphism property if there exists a net of unitary operators $\{u…