05.07.2017 um 17:15 Uhr in Raum 69/125
Prof. Dr. Zakhar Kabluchko (Westfälische Wilhelms-Universität Münster)
Convex Hulls of Random Walks: Expected Number of Faces
Let $X_1,...,X_n$ be independent identically distributed random vectors in $R^d$. We are interested in the convex hull of the random walk $0,S_1,\ldots,S_n$, where $S_k = X_1+\ldots+X_k$. We determine the expected number of $k$-dimensional faces of this random polytope. In particular, we show that under minor general position assumptions on the increments $X_i$, this number does not depend on the distribution of the increments. The problem of computing the expected number of faces will be reduced to the problem of computing the number of Weyl chambers of a reflection group intersected by a linear subspace in general position. This is joint work with Vladislav Vysotsky and Dmitry Zaporozhets.