Related papers: Lecture Notes on Random Matrix Theory
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
These lecture notes were prepared for a special topics course in the Department of Statistics at the University of Washington, Seattle. They comprise the first eight chapters of a book currently in progress.
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of…
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…