T. Tao

activity

19972023

most citedRandom matrices: Universality of local eigenvalue statistics up to the edge

276 citations · 4.5k across the 293 of their papers we have counts for

collaborators

Showing 2008 · math.PRShow all

3 papers · 2 filters

math.PR2008

From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices

Terence Tao, Van Vu

The famous \emph{circular law} asserts that if $M_{n}$ is an $n \times n$ matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution (ES…

math.PR2008★ 19 cited

Random matrices: Universality of ESDs and the circular law

Terence Tao, Van Vu, Manjunath Krishnapur

Given an $n \times n$ complex matrix $A$ , let $μ_{A} (x, y) := \frac{1}{n} ∣ {1 \leq i \leq n, ℜ λ_{i} \leq x, ℑ λ_{i} \leq y} ∣$ be the empirical spectral distribution (ESD) of its eige…

math.PR2008★ 3 cited

Smooth analysis of the condition number and the least singular value

Terence Tao, Van Vu

Let $\a$ be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of $\a$ and $M$ be a fixed matr…