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math.PR2020★ 2 cited
Fractional free convolution powers
Dimitri Shlyakhtenko, Terence Tao. With an appendix by David Jekel
The extension of the concept of a free convolution power to the case of non-integer was introduced by Bercovici-Voiculescu and Nica-Speicher,…
math.PR2015★ 9 cited
Free probability of type B and asymptotics of finite-rank perturbations of random matrices
D. Shlyakhtenko
We show that finite rank perturbations of certain random matrices fit in the framework of infinitesimal (type B) asymptotic freeness. This can be used to explain the appearance of…
math.PR2007
On Classical Analogues of Free Entropy Dimension
A. Guionnet, D. Shlyakhtenko
We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on $\mathb…