Related papers: Matricial model for the free multiplicative convol…
We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the…
We consider Hermite and Laguerre $\beta$-ensembles of large $N\times N$ random matrices. For all $\beta$ even, corrections to the limiting global density are obtained, and the limiting density at the soft edge is evaluated. We use the…
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
We study free topological groups defined over uniform spaces in some subclasses of the class NA of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free…
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Let G = Z2 act on a finite CW-complex X having mod 2 cohomology isomorphic to the product of quaternionic projective space and sphere HPn x Sm, n, m > or = 1. This paper is concerned with the connected fixed point sets and the orbit spaces…
We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an…
We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings.…
In this work, we introduce matrix-valued diffusion processes which describe the non-equilibrium situation of the matrix models for the beta-Hermite and the beta-Laguerre ensembles. We also study the corresponding spectral measure process…
Random noncommutative geometry can be seen as a Euclidean path-integral approach to the quantization of the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of investigating phase transitions in random…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
We show that the metric structure of morphisms $f\colon Y\to X$ between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton…
Let $\pi$ be an irreducible unitary representation of a finitely generated nonabelian free group $\Gamma$; suppose $\pi$ is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a…
We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define…
It is shown that the free multiplicative convolution of two nondegenerate probability measures on the unit circle has no continuous singular part relative to arclength measure. Analogous results have long been known for free additive…