A necklace of Wulff shapes

Research paper by Joël De Coninck, François Dunlop, Thierry Huillet

Indexed on: 20 May '05Published on: 20 May '05Published in: Mathematics - Probability


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.