Related papers: Lecture Notes on "Free Probability Theory"
This in an introduction to the theory of non-commutative distributions of non-commuting operators or random matrices. Starting from the basic problem to find a good approach to the meaning of "non-commutative distribution" we will, in…
This in an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigner's semicircle law,…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics,…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some…
These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
This is an introduction to some of the most probabilistic aspects of free probability theory.
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to…
Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
I give a survey about my work on combinatorial and probabilistic aspects of free probability theory. In particular, I present the combinatorial description of freeness in terms of free cumulants and I give some ideas of the main results of…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the…