Abstract:

Distributional limit theorems such as the Central Limit Theorem are important in statistics and probabilistic combinatorics. These kinds of theorems are usually stated asymptotically, with a topological notion of distributional convergence called weak convergence. A shortcoming of these theorems is that they are not quantitative. That is, they give no understanding of the rate of convergence.

Stein's method is a technique for bounding the distance between distributions in a variety of metrics consistent with weak convergence. We will introduce the idea with a simple proof of a quantitative version of the central limit theorem. We then turn to a more involved problem in probabilistic combinatorics. To approach this problem we will use Stein's method in combination with the idea of an exchangeable pair.

Speaker
Matthew Kwan
Research Area
Pure Maths Seminar
Affiliation
UNSW
Date
Tue, 20/05/2014 - 12:00pm
Venue
RC-4082, The Red Centre, UNSW