Spatial extent of N Brownian walkers

Statistical properties of the spatial extent of N Brownian walkers is
relevant to various physical situations like estimation of habitat
sizes of animal populations, disease spread in crop fields and river
pollution amongst others.

In the first part of my talk, I will focus on the distribution of the
size of the region visited and of the region overlapped by N
independent and identical one-dimensional Brownian walkers. Using a
connection between the spatial extent and extreme displacements I will
show, in the large N limit, that these distributions have interesting
limiting forms. These limiting forms are different from the standard
extreme value distributions of independent and identical random
variables. In the second part of my talk, I will discuss possible
generalizations to situations where the walkers are interacting.