Joint Dept. of Mathematics and CMSA Random Matrix & Probability Theory Seminar: Fluctuation bounds for O’Connell-Yor type systems


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March 31, 2021 2:00 pm - 3:00 pm
via Zoom Video Conferencing

Philippe Sosoe - Cornell University

The O'Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O'Connell, Yor and others, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds for the O'Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}.

In the second part of the talk, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models.

Joint work with Christian Noack and Benjamin Landon.