A Necklace of Wulff Shapes |
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| Authors: | Joël De Coninck François Dunlop Thierry Huillet |
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| Affiliation: | (1) Centre de Recherche en Modélisation Moléculaire, Université de Mons-Hainaut, 20 Place du Parc, 7000 Mons, Belgium;(2) Laboratoire de Physique Théorique et Modélisation (CNRS- UMR 8089), Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France |
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| Abstract: | In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density.AMS subject classification: 60K35, 60K37, 82B24, 82B41 |
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| Keywords: | Interfaces random substrate Wulff shape SOS model |
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