Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation

Baruch Meerson, Eytan Katzav, Arkady Vilenkin

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Using the weak-noise theory, we evaluate the probability distribution P(H,t) of large deviations of height H of the evolving surface height h(x,t) in the Kardar-Parisi-Zhang equation in one dimension when starting from a flat interface. We also determine the optimal history of the interface, conditioned on reaching the height H at time t. We argue that the tails of P behave, at arbitrary time t>0, and in a proper moving frame, as -lnP∼|H|5/2 and ∼|H|3/2. The 3/2 tail coincides with the asymptotic of the Gaussian orthogonal ensemble Tracy-Widom distribution, previously observed at long times.

Original languageAmerican English
Article number070601
JournalPhysical Review Letters
Issue number7
StatePublished - 19 Feb 2016

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© 2016 American Physical Society.


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