Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media
arXiv:1909.03841 · doi:10.1103/PhysRevE.101.012134
Abstract
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 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.
arXiv comment13 pages, 8 figures
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