Related papers: Free probability and random matrices

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of "second order freeness" and derive the global fluctuations of Gaussian and…

The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical…

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…

Let $a_{1},...,a_{n}, b_{1},...,b_{n}$ be random variables in some (non-commutative) probability space, such that $\{a_{1}, ..., a_{n} \}$ is free from $\{b_{1}, ..., b_{n} \}$. We show how the joint distribution of the $n$-tuple $(a_{1}…

In this paper, an analogue of matrix models from free probability is developed in the bi-free setting. A bi-matrix model is not simply a pair of matrix models, but a pair of matrix models where one element in the pair acts by…

This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the S-transform in the…

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…

Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the…

We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. We can relax the…

We study random band matrices within the framework of traffic probability, an operadic non-commutative probability theory introduced by Male based on graph operations. As a starting point, we revisit the familiar case of the permutation…

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…

Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone…

The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…

This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…

We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes…

We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random…

The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…

The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…

To a planar algebra P in the sense of Jones we associate a natural non- commutative ring, which can be viewed as the ring of non-commutative polynomials in several indeterminates, invariant under a symmetry encoded by P. We show that this…