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SUMMARY:Large deviations of surface height in the Kardar-Parisi-Zhang equa
tion
DTSTART;VALUE=DATE-TIME:20170905T080000Z
DTEND;VALUE=DATE-TIME:20170905T083000Z
DTSTAMP;VALUE=DATE-TIME:20230206T040800Z
UID:indico-contribution-160@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Baruch Meerson (Hebrew University of Jerusalem)\n\nT
he Kardar-Parisi-Zhang (KPZ) equation describes an important universality
class of nonequilibrium stochastic growth. There has been much recent inte
rest in the one-point probability distribution P(H\,t) of height H of the
evolving interface at time t. I will show how one can use the optimal fluc
tuation method (also known as the instanton method\, the weak-noise theory
\, the macroscopic fluctuation theory\, or simply WKB) to evaluate P(H\,t)
for different initial conditions in 1+1 dimensions. At short times the b
ody of the height distribution is Gaussian\, but its tails are non-Gaussia
n and highly asymmetric. In a moving frame\, one of the tails coincides\,
at all times\, with the proper tail of the Tracy-Widom distribution (for t
he flat and curved interface)\, and of the Baik-Rains distribution (for th
e stationary interface). The other tail displays a behavior that differs f
rom the known long-time asymptotic. At sufficiently large |H| this large-
deviation tail also persists at arbitrary long times. The case of station
ary interface is especially interesting. Here at short times the large dev
iation function of the height exhibits a singularity at a critical value o
f |H|. This singularity results from a symmetry-breaking of the "optimal p
ath" of the system\, and it has the character of a second-order phase tran
sition.\n\nhttps://zakopane.if.uj.edu.pl/event/4/contributions/160/
LOCATION:30
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/160/
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