Title
"Replica analysis of the one-dimensional Kardar-Parisi-Zhang equation"
Takashi Imamura (The University of Tokyo)
Abstract
The Kardar-Parisi-Zhang (KPZ) equation is a prototypical equation for the surface growth phenomena. Recently, the one-dimensional KPZ equation has attracted much attention in mathematical physics since the discovery of an exact solution for the height distribution by Sasamoto-Spohn and Amir-Corwin-Quastel in 2010.
In this poster, I will present our recent results on the exact height distribution for the stationary case (Phys. Rev. Lett. 108, 190603, 2012 and J. Stat. Phys. 150, 908, 2013) and the exact two-point height distribution function for the narrow-wedge initial data (arXiv:1305.1217). Our analysis is based on the replica approach developed by Kardar, Dotsenko and Calabrese-Le Doussal-Rosso, in which we utilize a remarkable connection of the KPZ equation with the delta Bose gas system. This is based on joint work with Tomohiro Sasamoto and Herbert Spohn.
