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arXiv · 2001.08919

Homogenization of ferromagnetic energies on Poisson random sets in the plane

Andrea Braides·Andrey Piatnitski
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Abstract

We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on proving that cells with `very long' or `very short' edges of the corresponding Voronoi tessellation can be neglected. In this way we may apply Geometry Measure Theory tools to define a compact convergence, and a characterisation of metric properties of clusters of Voronoi cells using limit theorems for subadditive processes.

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Andrea Braides, Andrey Piatnitski. 2020-01-24. Homogenization of ferromagnetic energies on Poisson random sets in the plane. https://arxiv.org/abs/2001.08919

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