Convex Hull of N planar Brownian Motions: Exact Results and an Application to Ecology

by Prof. Satya Majumdar (University of Paris)

Tuesday 2 Feb 2010, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

We compute exactly the mean perimeter and area of the convex hull of N independent planar Brownian paths each of duration T, both for open and closed paths. Surprisingly, the area and perimeter grows extremely slowly (logarithmically) with increasing population size N. This slow growth is a consequence of extreme value statistics and has interesting implication in ecological context in estimating the home range of a herd of animals with population size N.

Slides conhull_tifr.pdf