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SUMMARY:Variational methods for a singular SPDE yielding the universality 
 of the magnetisation ripple - Pavlos Tsatsoulis (Max-Planck-Institut\, Lei
 pzig)
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
UID:TALK157612@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The magnetisation ripple is a microstructure formed by the mag
 netisation in thin ferromagnetic films\, triggered by the random orientati
 on\nof the grains in a polycrystalline material. It is described by the mi
 nimisers of a non-convex energy functional. The corresponding Euler--Lagra
 nge equation\nis given by a singular elliptic SPDE in two dimensions drive
 n by white noise. On large scales\, the ripple exhibits a universal behavi
 our\, in the sense that it \ndoes not depend on the statistical model of t
 he grain distribution. In this talk\, I will address the universality of t
 he ripple based on a variational approach.\n\nFirst\, a suitable renormali
 sation of the random energy functional has to be preformed due to the roug
 hness of white noise. Then\, using the topology \nof $\\Gamma$-convergence
 \, one can give sense to the law of the renormalised energy functional\, w
 hich is independent of the way white noise is approximated. \nThis univers
 ality result holds in the class of (not necessarily Gaussian) approximatio
 ns to white noise satisfying the spectral gap inequality\, which\nallows u
 s to obtain sharp stochastic estimates.\n\nThe talk is based on a joint wo
 rk with Radu Ignat\, Felix Otto\, and Tobias Ried. 
LOCATION:Zoom
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