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math.PR2026
Infinite-variation Lévy processes are either strongly eroded or abrupt
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We prove that every real Lévy process of infinite variation is either abrupt or strongly eroded, resolving the conjectured geometric dichotomy on the smoothness of the convex hull…
math.PR2026
Generalised Random Parking for Trapeziums on a Strip
David Kramer-Bang, Stjepan Šebek
In this article, we study a generalisation of Rényi's car-parking problem in which isosceles trapeziums are sequentially deposited on a strip. We derive an explicit formula for the…
math.PR2026
Improved bounds on the inradius and inverse inradius process of the convex hull of planar Brownian motion
David Kramer-Bang, Hugo Panzo, Stjepan Šebek
We study the inradius and inverse inradius of the convex hull of standard planar Brownian motion. Our main goals are to improve the existing bounds on the expected values of these…