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SUMMARY:Bounds on the size of the convex hull of planar Brownian motion an
 d related inverse processes - Stjepan Šebek (University of Zagreb)
DTSTART:20240925T130000Z
DTEND:20240925T140000Z
UID:TALK220444@talks.cam.ac.uk
DESCRIPTION:In this talk\, we establish bounds on expected values of vario
 us geometric quantities that describe the size of the convex hull spanned 
 by a path of the standard planar Brownian motion. Expected values of the p
 erimeter and the area of the Brownian convex hull are known explicitly\, a
 nd satisfactory bounds on the expected value of its diameter can be found 
 in the literature as well. In this talk we investigate circumradius and in
 radius of the Brownian convex hull and obtain lower and upper bounds on th
 eir expected values. Our other goal is to find bounds on the related inver
 se processes (that correspond to the perimeter\, area\, diameter\, circumr
 adius and inradius of the convex hull) which provide us with some informat
 ion on the speed of growth of the size of the Brownian convex hull.
LOCATION:Seminar Room 2\, Newton Institute
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