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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 Å ebek
The paper derives improved bounds for the expected inradius and inverse inradius of the convex hull of planar Brownian motion, providing closed‑form expressions for related range s…
math.PR2024
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…
math.PR2024
Bounds on some geometric functionals of high dimensional Brownian convex hulls and their inverse processes
Hugo Panzo, Evan Socher
We prove two-sided bounds on the expected values of several geometric functionals of the convex hull of Brownian motion in and their inverse processes. This extends…