![[Search]](/static/images/search.gif){kind=small}
![[A-Z Index]](/static/images/az.gif){kind=small}
![[Contact]](/static/images/contact.gif){kind=small}
![[University of Cambridge]](/static/images/identifier2.gif){kind=small}
![[Talks.cam]](/static/images/talkslogosmall.gif)
Van Vu (Rutgers University)
Thursday 05 February 2009, 14:00-15:00
Random matrices: Universality of ESDs and the circular law
- đ¤ Speaker: Van Vu (Rutgers University)
- đ Date & Time: Thursday 05 February 2009, 14:00 - 15:00
- đ Venue: MR12
Abstract
Given an n by n complex matrix $A$, let \mu(A) be the empirical spectral distribution (ESD) of its eigenvalues $\lambda_i, i=1, ..., n$.
We consider the limiting distribution of the normalized ESD $\mu_{\frac{1}{\sqrt{n}} A_n}$ of a random matrix $A_n = (a_{ij})$ where the random variables $a{ij} – \E(a_{ij})$ are iid copies of a fixed random variable $x$ with unit variance. We prove the ``universality principle”, namely that the limit distribution in question is independent of the actual choice of $x$. In particular, in order to compute this distribution, one can assume that $x$ is real of complex gaussian.
As a corollary we establish the Circular Law conjecture in full generality. The proof combines ideas from several areas of mathematics: additive combinatorics, theoretical computer science, probability and high dimensional geometry.
Joint work with Terence Tao.
Series This talk is part of the Combinatorics Seminar series.
Included in Lists
- All CMS events
- All Talks (aka the CURE list)
- bld31
- CMS Events
- Combinatorics Seminar
- DPMMS info aggregator
- DPMMS lists
- DPMMS Lists
- DPMMS Pure Maths Seminar
- Hanchen DaDaDash
- Interested Talks
- MR12
- School of Physical Sciences
Note: Ex-directory lists are not shown.