6 papers
The Dyson equation for -positive maps and Hölder bounds for the Lévy distance of densities of states
Tobias Mai
The so-called density of states is a Borel probability measure on the real line associated with the solution of the Dyson equation which we set up, on any fixed -probabilit…
A Note on the Free and Cyclic Differential Calculus
Tobias Mai, Roland Speicher
In 2000, Voiculescu proved an algebraic characterization of cyclic gradients of noncommutative polynomials. We extend this remarkable result in two different directions: first, we…
The free field: realization via unbounded operators and Atiyah property
Tobias Mai, Roland Speicher, Sheng Yin
Let be operators in a finite von Neumann algebra and consider their division closure in the affiliated unbounded operators. We address the question when this divisi…
A note on existence of free Stein kernels
Guillaume Cébron, Max Fathi, Tobias Mai
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is…
Hölder Continuity of Cumulative Distribution Functions for Noncommutative Polynomials under Finite Free Fisher Information
Marwa Banna, Tobias Mai
This paper contributes to the current studies on regularity properties of noncommutative distributions in free probability theory. More precisely, we consider evaluations of selfad…
The free field: zero divisors, Atiyah property and realizations via unbounded operators
Tobias Mai, Roland Speicher, Sheng Yin
We consider noncommutative rational functions as well as matrices in polynomials in noncommuting variables in two settings: in an algebraic context the variables are formal variabl…