Colloquium, 9/14/2012

Thinning Random Partition Structures

Dr. Shannon Starr

Department of Mathematics
University of Alabama at Birmingham

14 September 2012
Shelby Center 218
3:00 (Refreshements at 2:30)

Abstract

Random partition structures were invented as a tool for the field of population genetics, but they also arise in simple models of finance, as well as statistical physics. Broadly they are in the subject of "random measures." It is a random sequence of positive numbers whose sum is (at most) 1. These represent the fraction of the whole of various market participants or allele/phenotype populations. The most natural and simple type of dynamics allows all the different participants to evolve independently. This was studied by Aizenman and Ruzmaikina in 2003 with further refinements by Arguin and then Shkolnikov. But a special case of this dynamics was not considered by those groups: where some participants leave the field entirely, or in the population model some species are extinguished. With Brigitta Vermesi and Ang Wei, we considered this problem and found some new behavior.