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math.PR2026
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 ,…
math.PR2026
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…
math.PR2026
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…