4 citations · 16 across the 17 of their papers we have counts for
18 papers
Weighted-threshold Coupon Collection
Sebastian Müller, Stjepan Šebek
We study a weighted-threshold version of the coupon collector problem in continuous time. Each type is discovered at rate and, once discovered, contributes weight ,…
On the convex hull of a planar Brownian bridge with a random Gaussian endpoint
Nikola Sandrić, Stjepan Šebek, Luka Šimek
We consider a one-parameter family of isotropic planar Gaussian processes \[ X_σ(t) =B_t+σt Z,\qquad 0\le t\le 1,\quad 0\le σ\le 1, \] where is a standard (-to-) planar B…
Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk
Rudi Mrazović, Hugo Panzo, Stjepan Šebek
We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objectives are to compute the expected perimeter and expected area of thi…
Convex hull of Brownian motion and Brownian bridge
Stjepan Šebek
In this article we study the convex hull spanned by the union of trajectories of a standard planar Brownian motion, and an independent standard planar Brownian bridge. We find exac…
On the convex hull of two planar random walks
Daniela Ivanković, Tomislav Kralj, Nikola Sandrić +1
In this paper, we study the limiting behavior of the perimeter and diameter functionals of the convex hull spanned by the first steps of two planar random walks. As the main re…
Predators and altruists arriving on jammed Riviera
Tomislav Došlić, Mate Puljiz, Stjepan Šebek +1
The Riviera model is a combinatorial model for a settlement along a coastline, introduced recently by the authors. Of most interest are the so-called jammed states, where no more h…
A model of random sequential adsorption on a ladder graph
Tomislav Došlić, Mate Puljiz, Stjepan Šebek +1
In random sequential adsorption (RSA), objects are deposited on a substrate randomly, irreversibly, and sequentially. Attempts of deposition that lead to an overlap with previously…
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…
Complexity Function of Jammed Configurations of Rydberg Atoms
Tomislav Došlić, Mate Puljiz, Stjepan Šebek +1
In this article, we determine the complexity function (configurational entropy) of jammed configurations of Rydberg atoms on a one-dimensional lattice. Our method consists of provi…
On a variant of Flory model
Tomislav Došlić, Mate Puljiz, Stjepan Šebek +1
We consider a one-dimensional variant of a recently introduced settlement planning problem in which houses can be built on finite portions of the rectangular integer lattice subjec…
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…
Packing density of combinatorial settlement planning models
Mate Puljiz, Stjepan Šebek, Josip Žubrinić
Recently, a combinatorial settlement planning model was introduced. The idea underlying the model is that the houses are randomly being built on a rectangular tract of land accordi…
Combinatorial settlement planning
Mate Puljiz, Stjepan Šebek, Josip Žubrinić
In this article, we consider a combinatorial settlement model on a rectangular grid where at least one side (east, south or west) of each house must be exposed to sunlight without…
Capacity of the range of random walks on groups
Rudi Mrazović, Nikola Sandrić, Stjepan Šebek
In this paper, we discuss asymptotic behavior of the capacity of the range of symmetric simple random walks on finitely generated groups. We show the corresponding strong law of la…
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…
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…