11 citations · 43 across the 15 of their papers we have counts for
17 papers
Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates
Tobias Mai, Roland Speicher
We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a l…
Computing the noncommutative inner rank by means of operator-valued free probability theory
Johannes Hoffmann, Tobias Mai, Roland Speicher
We address the noncommutative version of the Edmonds' problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calcula…
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…
Berry-Esseen bounds for the multivariate -free CLT and operator-valued matrices
Marwa Banna, Tobias Mai
We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asym…
Convergence for noncommutative rational functions evaluated in random matrices
Benoît Collins, Tobias Mai, Akihiro Miyagawa +2
One of the main applications of free probability is to show that for appropriately chosen independent copies of random matrix models, any noncommutative polynomial in these …
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…
Regularity of distributions of Wigner integrals
Tobias Mai
Wigner integrals and the corresponding Wigner chaos were introduced by P. Biane and R. Speicher in 1998 as a non-commutative counterpart of classical Wiener-Itô integrals and the c…
Applications of Realizations (aka Linearizations) to Free Probability
J. William Helton, Tobias Mai, Roland Speicher
We show how the combination of new "linearization" ideas in free probability theory with the powerful "realization" machinery -- developed over the last 50 years in fields includin…
Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension
Tobias Mai, Roland Speicher, Moritz Weber
We show that in a tracial and finitely generated -probability space existence of conjugate variables excludes algebraic relations for the generators. Moreover, under the as…
Absence of algebraic relations and of zero divisors under the assumption of finite non-microstates free Fisher information
Tobias Mai, Roland Speicher, Moritz Weber
We show that in a tracial and finitely generated -probability space existence of conjugate variables in an appropriate sense exclude algebraic relations for the generators.…
Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem
Serban Belinschi, Tobias Mai, Roland Speicher
We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just giv…
Operator-valued and multivariate free Berry-Esseen theorems
Tobias Mai, Roland Speicher
We address the question of a Berry-Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the o…
Free Deterministic Equivalents, Rectangular Random Matrix Models, and Operator-Valued Free Probability Theory
Roland Speicher, Carlos Vargas, Tobias Mai
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random m…