24 citations · 48 across the 17 of their papers we have counts for
4 papers · 1 filter
Convex hulls of random walks: Expected number of faces and face probabilities
Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets
Consider a sequence of partial sums , , starting at , whose increments are random vectors in , . We…
A multidimensional analogue of the arcsine law for the number of positive terms in a random walk
Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets
Consider a random walk , , whose increments are independent identically distributed random vectors in such that $…
Large deviations of convex hulls of planar random walks and Brownian motions
Arseniy Akopyan, Vladislav Vysotsky
We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give expli…
On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape
Arseniy Akopyan, Vladislav Vysotsky
We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that for any convex shape , there exist four poin…