Mirjana Vuletic, U Mass Boston
3:00 PM - 4:00 PM
The Schur process was introduced by Okounkov and Reshetikhin in 2003. This is one of the fundamental models in integrable probability. It has been generalized in many different ways and has many applications. Okounkov and Reshetikhin first used it to analyze a random plane partition model.
The Schur process is a class of measures on sequences of partitions where the first and last partitions are required to be empty. The free boundary Schur process is a generalization of the original process where the end partitions are free. This generalization encompasses a much wider class of models. Naturally, it is harder for the analysis, but allows us to analyze various random models in a unified approach and to understand the transitioning between models. We used a free fermion formalism to derive a Pfaffian formula for the correlation function. Further, we were able to analyze the correlation function kernel to study bulk and edge behavior of various random partition models, random tilings and last passage percolation models.
In this talk I will present our main results about the free boundary Schur process and its applications. This is a joint work with D. Betea, J. Bouttier, and P. Nejjar.
Event contact: arjun dot krishnan at rochester dot edu