Replica approach to the KPZ equation with half Brownian motion initial condition

Understand

We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process.

• We employ the replica Bethe ansatz and show that the generating function of the exponential moments of the height is expressed as a Fredholm determinant.
• From this the height distribution and its asymptotics are studied.
• Furthermore using the replica method we also discuss the multi-point height distribution.