Wednesday, January 13, 2021 - 12:30 in ZOOM - Video Conference
Variational methods for a singular SPDE yielding the universality of the magnetization ripple
A talk in the Bielefeld Stochastic Afternoon series by
Tobias Ried from MPI Leipzig
| Abstract: |
The magnetization ripple is a microstructure formed in thin ferromagnetic films due to the random orientation of the grains in a polycrystalline material. It can be described by minimizers of a non-convex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular.
In this talk I will show how variational methods based on Γ-convergence can be used to address the universal character of the magnetization ripple. Due to the infinite energy of the system, the (random) energy functional has to be renormalized. Using the topology of Γ-convergence, one can give a sense to the law of the renormalized functional that is independent of the way white noise is approximated. The universality holds in the class of (not necessarily Gaussian) approximations to white noise satisfying the spectral gap inequality, which allows us to obtain sharp stochastic estimates.
(Based on joint work with Radu Ignat, Felix Otto, and Pavlos Tsatsoulis)
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
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