Probing large deviations of the Kardar-Parisi-Zhang equation at short times with an importance sampling of directed polymers in random media.

Hartmann, Alexander K; Krajenbrink, Alexandre; Le Doussal, Pierre · Phys Rev E · 2020

basic_science · Level V

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Abstract

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang 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. The short-time behavior is investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations, showing a spectacular agreement with the analytical expressions. The flat and stationary initial conditions are studied in the full space, together with the droplet initial condition in the half-space.