Bounds on the size of the convex hull of planar Brownian motion and related inverse processes

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• Stjepan Šebek (University of Zagreb)
• Wednesday 25 September 2024, 14:00-15:00
• Seminar Room 2, Newton Institute.

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SSD - Stochastic systems for anomalous diffusion

In this talk, 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 values of the perimeter and the area of the Brownian convex hull are known explicitly, and satisfactory bounds on the expected value of its diameter can be found in the literature as well. In this talk we investigate circumradius and inradius of the Brownian convex hull and obtain lower and upper bounds on their expected values. Our other goal is to find bounds on the related inverse processes (that correspond to the perimeter, area, diameter, circumradius and inradius of the convex hull) which provide us with some information on the speed of growth of the size of the Brownian convex hull.

This talk is part of the Isaac Newton Institute Seminar Series series.

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