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CATEGORIES:Probability
SUMMARY:The smoothed KPZ equation in dimension three and h
igher: Edwards-Wilkinson regime of its fluctuation
s and its localization properties - Chiranjib Muk
herjee (Munster)
DTSTART;TZID=Europe/London:20181113T140000
DTEND;TZID=Europe/London:20181113T150000
UID:TALK110437AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/110437
DESCRIPTION:We study the Kardar-Parisi-Zhang equation in dimen
sion $d\\geq 3$ with space-time white noise which
is smoothed in space. There is a natural disorder
parameter attached to this equation which measures
the intensity of the noise. We show that when the
disorder is small\, the approximating solution co
nverges to a well-defined limit (with the limit de
pending on both the disorder and the mollification
procedure)\, while the re-scaled fluctuations con
verge to a Gaussian limit as predicted by the Edwa
rds-Wilkionson regime. \n\nWe also study the assoc
iated stochastic heat equation with multiplicative
noise\, which carries a natural Gaussian mutiplic
ative noise (GMC) on the Wiener space. When the di
sorder is large\, we also show that the total mass
of the GMC converges to zero\, while the endpoint
distribution of a Brownian path under the (renorm
laized) GMC measure is purely atomic. \n\nBased on
joint works with\, A. Shamov & O. Zeitouni\, F. C
omets & C. Cosco as well Y. Broeker.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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