Special P&A/Statistics/Biology Seminar: Random Convex Hulls and Extreme Value Statistics: Applications to Ecology and Animal Epidemics

 
Convex hull of a set of points in two dimensions roughly describes the

shape of the set. In this talk, I will discuss the statistical properties

of the convex hull for two stochastic processes in two dimensions: (i) a

set of n independent planar Brownian paths (ii) a branching Brownian

motion with death. We show how to compute exactly the mean perimeter and

the mean area of the convex hull in these two problems. The first problem

has application in estimating the home range of an animal population of

size n, while the second will be used to estimate the spatial extent of

the outbreak of animal epidemics. Our result also makes an interesting

connection between random geometry and extreme value statistics.
 
Date:
-
Location:
CP179
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