2 citations · 3 across the 4 of their papers we have counts for
9 papers
On the Hausdorff Continuity of Free Lèvy Processes and Free Convolution Semigroups
John D. Williams
Let denote a Borel probability measure and let denote the free additive convolution semigroup of Nica and Speicher. We show that the support of these me…
B-Valued Free Convolution for Unbounded Operators
John D. Williams
Consider the -valued probability space , where is a tracial von Neumann algebra. We extend the theory of operator valued f…
Operator-Valued Monotone Convolution Semigroups and an Extension of the Bercovici-Pata Bijection
Michael Anshelevich, John D. Williams
In a 1999 paper, Bercovici and Pata showed that a natural bijection between the classically, free and Boolean infinitely divisible measures held at the level of limit theorems of t…
Operator-valued Jacobi parameters and examples of operator-valued distributions
Michael Anshelevich, John D. Williams
In the setting of distributions taking values in a -algebra , we define generalized Jacobi parameters and study distributions they generate. These include nume…
Analytic Function Theory for Operator-Valued Free Probability
John D. Williams
It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized entirely in terms of their…
Quantum symmetric states on free product C*-algebras
Kenneth J. Dykema, Claus Köstler, John D. Williams
We introduce symmetric states and quantum symmetric states on universal unital free product C*-algebras an arbitrary unital C*-algebra A with itself infinitely many times, as a gen…