22 citations · 63 across the 16 of their papers we have counts for
22 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 and geometric flows for a class of nonlocal curvatures
Wojciech Cygan, Tomasz Grzywny, Julia Lenczewska
We consider a family of nonlocal curvatures determined through a kernel which is symmetric and bounded from above by a radial and radially non-increasing profile satisfying an inte…
Iterated-logarithm laws for convex hulls of random walks with drift
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek +1
We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero dr…
Bounds on the size of the convex hull of planar Brownian motion and related inverse processes
Wojciech Cygan, Hugo Panzo, Stjepan Šebek
We establish bounds on expected values of various geometric quantities that describe the size of the convex hull spanned by a path of the standard planar Brownian motion. Expected…
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…
Invariance principle for the capacity and the cardinality of the range of stable random walks
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
We prove an almost sure invariance principle for the capacity and the cardinality of the range of a class of -stable random walks on the integer lattice with $d/α…
Functional CLT for the range of stable random walks
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
In this note, we establish a functional central limit theorem for the capacity of the range for a class of -stable random walks on the integer lattice with $d > 5…
CLT for the capacity of the range of stable random walks
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
In this article, we establish a central limit theorem for the capacity of the range process for a class of -dimensional symmetric -stable random walks with the index satisfyi…
Transition probability estimates for subordinate random walks
Wojciech Cygan, Stjepan Šebek
Let be the simple random walk on the integer lattice . For a Bernstein function we consider a random walk which is subordinated to . Under a ce…
On recurrence of the multidimensional Lindley process
Wojciech Cygan, Judith Kloas
A Lindley process arises from classical studies in queueing theory and it usually reflects waiting times of customers in single server models. In this note we study recurrence of i…
A note on the generalized heat content for Lévy processes
Wojciech Cygan, Tomasz Grzywny
Let be a Lévy process in and be an open subset of with finite Lebesgue measure. The quantity $H (t) = \int_Ω \mathb…
On the rate of convergence in the central limit theorem for hierarchical Laplacian
Alexander Bendikov, Wojciech Cygan
Let be a proper ultrametric space. Given a measure on and a function defined on the set of all non-singleton balls we consider the hierarchical Laplacian…
Oscillating heat kernels on ultrametric spaces
Alexander Bendikov, Wojciech Cygan, Wolfgang Woess
Let be a proper ultrametric space. Given a measure on and a function defined on the collection of all non-singleton balls of , we consider t…
Heat content for convolution semigroups
Wojciech Cygan, Tomasz Grzywny
Let be a Lévy process in and be an open subset of with finite Lebesgue measure. In this article we consider the qua…
Asymptotic behavior of densities of unimodal convolution semigroups
Wojciech Cygan, Tomasz Grzywny, Bartosz Trojan
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on under the assumption that its L…
Limit theorems for random walks
Alexander Bendikov, Wojciech Cygan, Bartosz Trojan
We consider a random walk which is obtained from the simple random walk by a discrete time version of Bochner's subordination. We prove that under certain conditions on t…
On massive sets for subordinated random walks
Alexander Bendikov, Wojciech Cygan
We study massive (reccurent) sets with respect to a certain random walk defined on the integer lattice , . Our random walk is obtained from the si…
Alpha-stable random walk has massive thorns
Alexander Bendikov, Wojciech Cygan
We introduce and study a class of random walks defined on the integer lattice -- a discrete space and time counterpart of the symmetric -stable process in $\mat…