A necklace of Wulff shapes

Details A necklace of Wulff shapes A necklace of Wulff shapes

2005-05-20

arxiv.org/abs/math/0505439v1

Mathematics

Probability

Scientific paper

10.1007/s10955-005-8019-5

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.

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