Date:
-
Location:
CP179
Speaker(s) / Presenter(s):
Satya Majumdar (University of Paris, Orsay)
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.
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.