Macdonald Processes and Some Applications in Probability and Integrable Systems

Joint Princeton Mathematical Physics Seminar
Topic:Macdonald Processes and Some Applications in Probability and Integrable Systems
Speaker:Ivan Corwin
Affiliation:Microsoft Research & Massachusetts Institute of Technology
Date:Tuesday, November 29
Time/Room:4:30pm - 5:30pm/S-101

Macdonald processes are probability measures on sequences of partitions de?ned in terms of nonnegative specializations of the Macdonald symmetric functions and two parameters q, t ? [0,1). Utilizing the Macdonald difference operators we prove several results about observables these processes, including Fredholm determinant formulas for q-Laplace transforms. Taking limits and degenerations we arrive at new results in the study of certain directed polymers, branching processes, quantum many body systems, interacting particle systems and stochastic PDEs. This is based on joint work with Alexei Borodin.