Integrable probability

School of Mathematics Colloquium
Tuesday, January 16, 2018 - 11:05
1 hour (actually 50 minutes)
Skiles 006
Columbia University
The probability of outcomes of repeated fair coin tosses can be computed exactly using binomial coefficients. Performing asymptotics on these formulas uncovers the Gaussian distribution and the first instance of the central limit theorem. This talk will focus on higher version of this story. We will consider random motion subject to random forcing. By leveraging structures from representation theory and quantum integrable systems we can compute the analogs of binomial coefficients and extract new and different asymptotic behaviors than those of the Gaussian. This model and its analysis fall into the general theory of "integrable probability".