title: Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation.
abstract: 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.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Baruch
authors.initials: B
authors.lastname: Meerson
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Eytan
authors.initials: E
authors.lastname: Katzav
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Arkady
authors.initials: A
authors.lastname: Vilenkin