An introduction to random matrix theory

TL;DR

This paper provides an accessible introduction to the fundamental concepts and results of random matrix theory, aimed at students from diverse fields with minimal background in probability.

Contribution

It offers a comprehensive overview of basic random matrix theory results and motivations suitable for a broad audience with limited prior knowledge.

Findings

Introduces key results of random matrix theory

Connects theory to applications in statistics and finance

Provides educational lecture notes for beginners

Abstract

These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of random matrix theory and some of its motivations, targeted to a large panel of students coming from statistics, finance, etc. Only a small background in probability is required.