Lah distributions, Stirling numbers, and phase transitions for convex hulls of random walks
21 квітня 2021 року о 14 год 15 хв Let \(X_1,X_2,\ldots\) be independent random vectors in \(\mathbb{R}^d\) having an absolutely continuous distribution. Consider the random walk \(S_k:=X_1+\ldots+X_k\), and let \(P_n:={\rm conv}\{0,S_1,S_2,\ldots,S_n\}\) be the convex hull of its first \(n\) steps. We shall be interested in the number of the \(k\)-dimensional faces of the polytope \(P_n\)…