Lecture Notes on Free Probability
by Vladislav Kargin
Publisher: arXiv 2013
Number of pages: 100
Description:
Contents: Non-commutative Probability Spaces; Distributions; Freeness; Asymptotic Freeness of Random Matrices; Asymptotic Freeness of Haar Unitary Matrices; Free Products of Probability Spaces; Law of Addition; Limit Theorems; Multivariate CLT; Infinitely-Divisible Distributions; Multiplication and S-transform; Products of free random variables; Free Cumulants; Non-crossing partitions and group of permutations; Fundamental Properties of Free Cumulants; Free Cumulants; R-diagonal variables; Brown measure of R-diagonal variables.
Download or read it online for free here:
Download link
(650KB, PDF)
Similar books
An Introduction to Probability and Random Processesby Gian-Carlo Rota, Kenneth Baclawski
The purpose of the text is to learn to think probabilistically. The book starts by giving a bird's-eye view of probability, it first examines a number of the great unsolved problems of probability theory to get a feeling for the field.
(14205 views)
Probability, Random Processes, and Ergodic Propertiesby Robert M. Gray - Springer
A self-contained treatment of the theory of probability, random processes. It is intended to lay theoretical foundations for measure and integration theory, and to develop the long term time average behavior of measurements made on random processes.
(9841 views)
Radically Elementary Probability Theoryby Edward Nelson - Princeton University Press
In this book Nelson develops a new approach to probability theory that is just as powerful as but much simpler than conventional Kolmogorov-style probability theory used throughout mathematics for most of the 20th century.
(13220 views)
Advanced Topics in Probabilityby S.R.S. Varadhan - New York University
Topics: Brownian Motion; Diffusion Processes; Weak convergence and Compactness; Stochastic Integrals and Ito's formula; Markov Processes, Kolmogorov's equations; Stochastic Differential Equations; Existence and Uniqueness; Girsanov Formula; etc.
(6110 views)