31 citations · 62 across the 18 of their papers we have counts for
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Bi-Free Extreme Values
Hao-Wei Huang, Jiun-Chau Wang
In this paper, we continue Voiculescu's recent work on the analogous extreme value theory in the context of bi-free probability theory. We derive various equivalent conditions for…
Harmonic analysis for the bi-free partial S-transform
Hao-Wei Huang, Jiun-Chau Wang
This is a continuation of our previous work in bi-free harmonic analysis for commuting left and right variables. Here we analyze the bi-free partial S-transform and use the results…
Analytic aspects of the bi-free partial R-transform
Hao-Wei Huang, Jiun-Chau Wang
Since Voiculescu introduced his bi-free probability theory in 2013, the major development of the theory has been on its combinatorial side; in particular, on the combinatorics of b…
On multiplicative conditionally free convolution
Mihai Popa, Jiun-Chau Wang
Using the combinatorics of non-crossing partitions, we construct a conditionally free analogue of the Voiculescu's S-transform. The result is applied to analytical description of c…
Limit theorems for additive c-free convolution
Jiun-Chau Wang
In this paper we find necessary and sufficient conditions for the weak convergence of c-free convolution of pairs of measures, where the measures are assumed to be infinitesimal an…
On freely indecomposable measures
Hari Bercovici, Jiun-Chau Wang
We show that a probability measure is not a nontrivial free additive convolution if it puts no mass in an interval whose endpoints are atoms. The analogous results for free multipl…
Limit laws for boolean convolutions
Jiun-Chau Wang
We study the distributional behavior for products, and for sums of boolean independent random variables in an infinitesimal triangular array. We show that the limit laws of boolean…
The asymptotic behavios of free convolution
Hari Bercovici, Jiun-Chau Wang
We give a streamlined proof of the limit theorems for the free additive convolution of infinitesimal triangular arrays of probability measures on the real line. The result was firs…
Limit theorems for free multiplicative convolutions
Hari Bercovici, Jiun-Chau Wang
We determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. In the case of positive variables, the main theorem exte…