TY - JOUR

T1 - Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation

AU - Meerson, Baruch

AU - Katzav, Eytan

AU - Vilenkin, Arkady

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/2/19

Y1 - 2016/2/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84959440786&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.116.070601

DO - 10.1103/PhysRevLett.116.070601

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AN - SCOPUS:84959440786

SN - 0031-9007

VL - 116

JO - Physical Review Letters

JF - Physical Review Letters

IS - 7

M1 - 070601

ER -