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Lecture 2: Random discrete matrices II: Random walks, lazy random walks and the singularity problem | Einstein Institute of Mathematics

Lecture 2: Random discrete matrices II: Random walks, lazy random walks and the singularity problem

Date: 
Fri, 25/05/200711:00-13:00
Location: 
Room 110
Lecturer: 
Prof. Van H. Vu (Rutgers University)
I will discuss recent developments concerning the following question:
"What is the probability that a random Bernoulli matrix is singular ?"

The conjectured bound here is (1/2+o(1))n, basically the probability that there are two equal rows. In 1995, Kahn, Komlos and Szemeredi proved the first exponential bound .999n. Few years ago, Tao and I improved the bound to (3/4+o(1))n, based on an inverse theorem about the returning probability of a random walk. I will focus on this bound but also discuss few even more recent improvements and extensions.