Crossover distributions at the edge of the rarefaction fan

Understand

We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $\rho_-<\rho_+$ so that macroscopically one has a rarefaction fan.

• We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf--Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data.
• For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm.
• Pure Appl.