Combinatorial problems in random matrix theory
Van H. Vu
Dept. of Mathematics, Rutgers University, New Jersey, USA
Dept. of Mathematics, Rutgers University, New Jersey, USA
2009/12/21 Mon, 3PM-4PM (E6-1, Room 2412)
I am going to give a survey on several basic problems of combinatorial nature concerning random Bernoulli matrices, including:
(1) The singularity problem: What is the probability that a random Bernoulli matrix is singular?
(2) The determinant problem: What is the typical value of the determinant?
(3) The permanent problem: What is the typical value of the permanent?
(4) The eigenvector problem: How does a typical eigenvector look like?
If time allows, I will discuss connections to other areas of mathematics, most importantly additive combinatorics.