Seminar Event Detail

Integrable Systems and Random Matrix Theory

Date:  Monday, April 02, 2018
Location:  1866 East Hall (4:00 PM to 5:00 PM)

Title:  Lower tail of the KPZ equation

Abstract:   Over the last decade, KPZ equation gained immense attention for variety of of different reasons. From this perspective, tail probabilities of the one point distribution of the KPZ equation are important. However, the exact rate of decay was unknown. To illustrate its complexity, let us mention that an optimal bounds on the lower tail probability of the one point distribution of the KPZ equation under narrow wedge initial condition needs solving an infinite dimensional Riemann-Hilbert problem. In this talk, I will demonstrate how one can avoid such difficulties and still get (almost) tight upper and lower bounds on the lower tail probability of the narrow wedge solution. Our results make use of the recent work of Thomas Bothner on the Ablowitz-Segur solution of the second Painleve equation and stochastic Airy operator.

This is a joint work with my advisor Prof. Ivan Corwin. If time permits, I will discuss few more interesting facets like tail bounds under general initial conditions, large deviation of the lower tail of the narrow wedge solution, tail bounds of other integrable models etc.


Speaker:  Promit Ghosal
Institution:  Columbia University

Event Organizer:   Guilherme Silva


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