V. Vu

activity

20002023

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

276 citations · 1k across the 68 of their papers we have counts for

collaborators

Showing 2005Show all

5 papers · 1 filter

math.PR2005★ 1 cited

Inverse Littlewood-Offord theorems and the condition number of random discrete matrices

Terence Tao, Van Vu

Consider a random sum $η_{1} v_{1} + ... + η_{n} v_{n}$ , where $η_{1}, ..., η_{n}$ are i.i.d. random signs and $v_{1}, ..., v_{n}$ are integers. The Littlewood-Offord problem asks to maximize concentr…

math.NT2005★ 4 cited

Olson's theorem for cyclic groups

V. Vu

Let $n$ be a large number. A subset $A$ of $Z_{n}$ is complete if $S_{A} = Z_{n}$ , where $S_{A}$ is the collection of the subset sums of $A$ . Olson proved that if $n$ is a prime and $|A|>…

math.PR2005★ 9 cited

Random symmetric matrices are almost surely non-singular

Kevin Costello, Terence Tao, Van Vu

Let $Q_{n}$ denote a random symmetric $n$ by $n$ matrix, whose upper diagonal entries are i.i.d. Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove…

math.PR2005

Central limit theorems for random polytopes in a smooth convex set

Van Vu

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ random points in $K$ independently according to the uniform distribution. The convex hull of these points, de…

math.CO2005

On the singularity probability of random Bernoulli matrices

Terence Tao, Van Vu

Let $n$ be a large integer and $M_{n}$ be a random $n$ by $n$ matrix whose entries are i.i.d. Bernoulli random variables (each entry is $\pm 1$ with probability 1/2). We show that th…