7 citations · 28 across the 11 of their papers we have counts for
11 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…
Free-Boolean independence for pairs of algebras
Weihua Liu
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras…
General de Finetti type theorems in noncommutative probability
Weihua Liu
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of…
Quantum Observable Generalized Orthoalgebras
Qiang Lei, Weihua Liu, Zhe Liu +1
Let denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space , which is the set of all physical quantities on…
Extended de Finetti theorems for boolean independence and monotone independence
Weihua Liu
We construct several new spaces of quantum sequences and their quantum families of maps in sense of Sołtan. Then, we introduce noncommutative distributional symmetries associated w…
A noncommutative De Finetti theorem for boolean independence
Weihua Liu
We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for…