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SUMMARY:Convex Hulls of Two Dimensional Stochastic Processes - Satya Majum
 dar (Université Paris Saclay)
DTSTART:20230726T100000Z
DTEND:20230726T110000Z
UID:TALK203161@talks.cam.ac.uk
DESCRIPTION:Convex hull of a set of points in two dimensions roughly descr
 ibes the shape of the set. In this talk\, I will discuss the statistical p
 roperties of the convex hull of several stochastic processes in two dimens
 ions. By adapting Cauchy's formula to random curves\, we develop a formali
 sm to compute explicitly the mean perimeter and the mean area of the conve
 x hull of arbitrary two dimensional stochastic processes of a fixed durati
 on. Our result makes an interesting and general connection between random 
 geometry and extreme value statistics. I will discuss two examples in deta
 il (i) a set of n independent planar Brownian paths (ii) planar branching 
 Brownian motion with death. The first problem has application in estimatin
 g the home range of an animal population of size n\, while the second is u
 seful to estimate the spatial extent of the outbreak of animal epidemics. 
 Finally I will also discuss two other recent examples of planar stochastic
  processes: (a) active run-and-tumble process and (b) resetting Brownian m
 otion.
LOCATION:Seminar Room 2\, Newton Institute
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