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CATEGORIES:Probability
SUMMARY:Variational methods for a singular SPDE yielding t
he universality of the magnetisation ripple - Pavl
os Tsatsoulis (Max-Planck-Institut\, Leipzig)
DTSTART;TZID=Europe/London:20210223T140000
DTEND;TZID=Europe/London:20210223T150000
UID:TALK157612AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/157612
DESCRIPTION:The magnetisation ripple is a microstructure forme
d by the magnetisation in thin ferromagnetic films
\, triggered by the random orientation\nof the gra
ins in a polycrystalline material. It is described
by the minimisers of a non-convex energy function
al. The corresponding Euler--Lagrange equation\nis
given by a singular elliptic SPDE in two dimensio
ns driven by white noise. On large scales\, the ri
pple exhibits a universal behaviour\, in the sense
that it \ndoes not depend on the statistical mode
l of the grain distribution. In this talk\, I will
address the universality of the ripple based on a
variational approach.\n\nFirst\, a suitable renor
malisation of the random energy functional has to
be preformed due to the roughness of white noise.
Then\, using the topology \nof $\\Gamma$-convergen
ce\, one can give sense to the law of the renormal
ised energy functional\, which is independent of t
he way white noise is approximated. \nThis univers
ality result holds in the class of (not necessaril
y Gaussian) approximations to white noise satisfyi
ng the spectral gap inequality\, which\nallows us
to obtain sharp stochastic estimates.\n\nThe talk
is based on a joint work with Radu Ignat\, Felix O
tto\, and Tobias Ried.
LOCATION:Zoom
CONTACT:Perla Sousi
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