Student Probability Seminar

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The lower tail probability of the half-space KPZ equation

Speaker: Yujin Kim, CIMS

Location: Online

Date: Wednesday, April 14, 2021, 9 a.m.

Synopsis:

The half-space KPZ equation is a paradigmatic model in a class of 1+1 dimensional random growth models subject to a boundary, known as the half-space KPZ universality class, whose solution has been shown to arise as the long time limit under weak asymmetric scaling of many of the models in this universality class. However, compared to the usual (full-space) KPZ equation, much less is understood. In this talk, we discuss novel bounds on the lower-tail of the solution to the half-space KPZ equation obtained via an intimate connection with the GOE point process. Along the way, we will establish bounds on the upper and lower large deviations of the GOE point process on intervals. Our methods involve connections to Pfaffian point processes, the stochastic Airy operator, the thinned GOE point process, and the Painlevé II equation.