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dc.contributor.authorToninelli, Fabio Lucio
HAL ID: 17419
ORCID: 0000-0003-1710-8811
dc.contributor.authorSimenhaus, François
dc.contributor.authorLacoin, Hubert
dc.subjectCurve-shortening flowen
dc.subjectGlauber dynamicsen
dc.subjectsing modelen
dc.titleZero-temperature 2D stochastic Ising model and anisotropic curve-shortening flowen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire de Physique de l'ENS Lyon (Phys-ENS) CNRS : UMR5672 – École Normale Supérieure de Lyon;France
dc.description.abstractenLet D be a simply connected, smooth enough domain of R2. For L > 0 consider the continuous time, zero-temperature heat bath dynamics for the nearest-neighbor Ising model on Z2 with initial condition such that σx = −1 if x ∈ LD and σx = +1 otherwise. It is conjectured [24] that, in the diffusive limit where space is rescaled by L, time by L2 and L → ∞, the boundary of the droplet of "−" spins follows a deterministic anisotropic curve-shortening flow, where the normal velocity at a point of its boundary is given by the local curvature times an explicit function of the local slope. The behavior should be similar at finite temperature T < Tc, with a different temperature-dependent anisotropy function. We prove this conjecture (at zero temperature) when D is convex. Existence and regularity of the solution of the deterministic curve-shortening flow is not obvious a priori and is part of our result. To our knowledge, this is the first proof of mean curvature-type droplet shrinking for a model with genuine microscopic dynamics.en
dc.relation.isversionofjnlnameJournal of the European Mathematical Society
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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