43 citations · 229 across the 31 of their papers we have counts for
22 papers · 1 filter
Fock representation of free convolution powers
Michael Anshelevich, Jacob Mashburn
Let be a star-algebra with a state , and . Through a Fock space construction, we define two states and on the tensor algebra such that under the…
Some Fock spaces with depth two action
Michael Anshelevich, Jacob Mashburn
The subject of this paper are operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from arXiv:math/0702158,…
Higher variations for free Lévy processes
Michael Anshelevich, Zhichao Wang
For a general free Lévy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the Lévy-Itô representation…
Product formulas on posets, Wick products, and a correction for the -Poisson process
Michael Anshelevich
We give an example showing that the product and linearization formulas for the Wick product versions of the -Charlier polynomials in (Anshelevich 2004) are incorrect. Next, we o…
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…