Related papers: Lecture Notes on Random Matrix Theory
Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
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 for a graduate-level introductory course on singularity categories.
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.
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 is a series of lecture notes explaining topos theory and its application in physics.
Lecture notes for an introductory course in elementary particles.
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…
In joint work with Adam Black and Reuben Drogin, we develop a new approach to understanding the diffusive limit of the random Schrodinger equation based on ideas taken from random matrix theory. These lecture notes present the main ideas…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
These are lecture notes on string theory at Fudan University.
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
These are notes from my lecture at 4ECM in Stockholm (June 2004).
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…
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.