Notice
Fluctuations of random convex interfaces
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Descriptif
We consider the convex hull of a point set constituted with independent and uniformly distributed points in a smooth convex body K of R^d. We show that the rescaled maximal radial fluctuation as well as maximal facet area follow asymptotically a Gumbel extreme value distribution as the size of the input goes to infinity. These results rely in particular on the study of a so-called typical facet of the random polytope. In particular, the rates of convergence are similar to those observed for a large variety of random interfaces in probability theory (random cluster models, oriented random walks…). This is joint work with J. E. Yukich.
Thème
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