Shishen Lin

Shishen Lin

I am a PhD student of Computer Science at Birmingham. I mainly focus on Artificial Intelligence, Optimisation, Evolutionary Algorithm.

A Brief Overview on Random Matrix Theory

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Introduction to Wigner Semicircle Theorem

This is a brief introduction on Random Matrix Theory (RMT). We first present the one of the main theorems in RMT.

Let $( M_{n} )^{\infty}_{n=1}$ be a sequence of Wigner matrices and for each $n$, denoted by $X_{n}=M_{n}/\sqrt{n}$, then $\mu _{X_{n}}$ converges weakly to the semicircle distribution, \begin{equation} \sigma (x) dx = \frac{1}{2\pi } \sqrt{4-x^2} \mathbf{1}_{\{|x|\leq 2\}}dx, \end{equation}