8 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 …
Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk
Rudi MrazoviÄ, Hugo Panzo, Stjepan Å ebek
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…
On the convex hull of a planar Brownian bridge with a random Gaussian endpoint
Nikola SandriÄ, Stjepan Å ebek, Luka Å imek
We consider a one-parameter family of isotropic planar Gaussian processes \[ X_Ï(t) =B_t+Ït Z,\qquad 0\le t\le 1,\quad 0\le Ï\le 1, \] where is a standard (-to-) plana…
On the convex hull of two planar random walks
Daniela IvankoviÄ, Tomislav Kralj, Nikola SandriÄ +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…
A model of random sequential adsorption on a ladder graph
Tomislav DoÅ¡liÄ, Mate Puljiz, Stjepan Å ebek +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…
Bounds on the size of the convex hull of planar Brownian motion and related inverse processes
Wojciech Cygan, Hugo Panzo, Stjepan Å ebek
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…