22 research outputs found
Large deviations of the interface height in the Golubovi\'{c}-Bruinsma model of stochastic growth
We study large deviations of the one-point height distribution,
, of a stochastic interface, governed by the
Golubovi\'{c}-Bruinsma equation where is the interface height at point and time , and
is the Gaussian white noise. The interface is initially flat, and
is defined by the relation . Using the optimal fluctuation
method (OFM), we focus on the short-time limit. Here the typical fluctuations
of are Gaussian, and we evaluate the strongly asymmetric and non-Gaussian
tails of . We show that the upper tail scales as . The lower tail, which scales as , coincides with its counterpart for the
Kardar-Parisi-Zhang equation, and we uncover a simple physical mechanism behind
this universality. Finally, we verify our asymptotic results for the tails, and
compute the large deviation function of , numerically.Comment: 8 pages, 8 figure