Promit Ghosal

[Balint Virag]

Monday, April 10, 2:10pm

Fields Institute Room 210

Promit Ghosal

NYU

Lower tail of the KPZ equation.

Large deviation of stochastic PDEs are important in many aspect.
In this talk, I will demonstrate how 1-d Coulomb gas electrostatics
provides precise control over the left tail of the KPZ
(Kardar-Parisi-Zhang) equation for the narrow wedge initial condition. Our
analysis exploits an exact connection between the KPZ one-point
distribution and the Airy point process. This enables us to establish a
large deviation principle for the left tail.  In addition, we provide
rigorous proof of finite-time tail bounds on the KPZ distribution which
bespeaks a crossover between exponential decay with exponent 3  (in the
shallow left tail) to exponent 5/2 (in the deep left tail).

 This talk will be mainly based on a joint work with my adviser Ivan
Corwin. If time permits, I will talk about our ongoing work on the tail
probabilities of the KPZ under general initial condition and tails of other
integrable models like ASEP, stochastic six vertex model etc.