4 citations · 11 across the 4 of their papers we have counts for
8 papers
The atoms of the free additive convolution of two operator-valued distributions
Serban Belinschi, Hari Bercovici, Weihua Liu
Suppose that and are two selfadjoint random variables that are freely independent over an operator algebra . We describe the possible operator atoms…
An Operad of Non-commutative Independences Defined by Trees
David Jekel, Weihua Liu
We study -ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal…
Relations between convolutions and transforms in operator-valued free probability
Weihua Liu
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relat…
Operator valued random matrices and asymptotic freeness
Weihua Liu
We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of…
Free-free-Boolean independence for triples of algebras
Weihua Liu
In this paper, we introduce the notion of free-free-Boolean independence relation for triples of algebras. We define free-free-Boolean cumulants ans show that the vanishing of mixe…
Free-Boolean independence with amalgamation
Weihua Liu, Ping Zhong
In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean…