11 papers
Fluctuations for diameter and perimeter of convex hulls of multiple random walks
Wojciech Cygan, Tomislav Kralj, Nikola Sandrić +3
We study the diameter and perimeter of the convex hull generated by finitely many independent planar random walks whose increments have finite second moments. The large-time fluctu…
Alexandrov Theorem for nonlocal curvature
Wojciech Cygan, Tomasz Grzywny
In this article we obtain a nonlocal version of the Alexandrov Theorem which asserts that the only set with sufficiently smooth boundary and of constant nonlocal mean curvature is…
Asymptotics of non-local perimeters
Wojciech Cygan, Tomasz Grzywny
We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on which integrates the function . Such defini…
Convex hulls of stable random walks
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in . We prove convergence of the convex hull in the space of a…
Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials
Wojciech Cygan, Kamil Kaleta, Mateusz Śliwiński
We propose and study a certain discrete time counterpart of the classical Feynman--Kac semigroup with a confining potential in countable infinite spaces. For a class of long range…
Limit theorems for a stable sausage
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
In this article, we study fluctuations of the volume of a stable sausage defined via a -dimensional rotationally invariant -stable process. As the main results, we establish…