High-precision simulation of the height distribution for the KPZ equation

Understand

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature.

• Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails.
• Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations.
• At short times the agreement with the analytical expression is spectacular.