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Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field
recentered maximum two-dimensional discrete Gaussian Free Field
2010/12/8
We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long–standing conjecture. The proof c...
Global Minimizers for Free Energies of Subcritical Aggregation Equations with Degenerate Diffusion
Global Minimizers Free Energies of Subcritical Aggregation Equations Degenerate Diffusion
2010/12/14
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on Rd. Such equations arise in mathematical biology as mo...