Related papers: Partial freeness of random matrices
We investigate the concept of orbital free entropy from the viewpoint of matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation…
We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called…
We address the question of the asymptotic description of random tensors that are local-unitary invariant, that is, invariant by conjugation by tensor products of independent unitary matrices. We consider both the mixed case of a tensor with…
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 free harmonic analysis (such as subordination functions…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of cumulants in probability theory. We review this theory, and…
In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a…
The asymptotic freeness of independent unitarily invariant $N\times N$ random matrices holds in expectation up to $O(N^{-2})$. An already known consequence is the infinitesimal freeness in expectation. We put in evidence another consequence…
It is well known that, under some assumptions, the limit distribution of random block matrices and their partial transposition converges to the distributions of random variables in some noncommutative probability space. Using free…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
We prove that independent rectangular random matrices, when embedded in a space of larger square matrices, are asymptotically free with amalgamation over a commutative finite dimensional subalgebra $D$ (under an hypothesis of unitary…
We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as a D-probability space as well. Let X be in M. We characterize freeness of X from B with amalgamation over D in terms of a certain…
This note examines the implications of randomly selecting vectors from an infinite-dimensional Hilbert space on linear independence, assuming that for all $k$, the first $k$ vectors follow an absolutely continuous law with respect to a…
We pursue the current developments in random tensor theory by laying the foundations of a free probability theory for tensors and establish its relevance in the study of random tensors of high dimension. We give a definition of freeness…
We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical…