# Concentration and Anti-Concentration

Monday, September 8, 2014 - 10:15am - 11:05am

Keller 3-180

Van Vu (Yale University)

In probabilistic combinatorics, one often needs to have some rough estimate for the distribution of a complicated random variable. There are two main kinds of estimates:

(1) Concentration: If one take an interval I far from the mean, then the probability that X in I is very small.

(2) Anti-concentration: If one take a short interval I, then the probability that X in I is also very small.

I am going to discuss a few recent results in these areas, together with applications. Most of the talk will be based on my papers Small Ball Probability with H. Nguyen, and Random Weighted projections with K. Wang, available on the arxiv.

(1) Concentration: If one take an interval I far from the mean, then the probability that X in I is very small.

(2) Anti-concentration: If one take a short interval I, then the probability that X in I is also very small.

I am going to discuss a few recent results in these areas, together with applications. Most of the talk will be based on my papers Small Ball Probability with H. Nguyen, and Random Weighted projections with K. Wang, available on the arxiv.

MSC Code:

60C05

Keywords: