Convex hull of N planar Brownian motions: exact results and an application to ecology.

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. We show that the mean perimeter =alpha N sqrt[T] and the mean area =beta(N)T for all T. The prefactors alpha N and beta N, computed exactly for all N, increase very slowly (logarithmically) with increasing N. This slow growth is a consequence of extreme value statistics and has interesting implications in an ecological context in estimating the home range of a herd of animals with a population size N.

• Publication year

  2009

• Venue

  Physical Review Letters

• Publication date

  2009-07-06

• Fields of study

  Mathematics, Physics, Medicine, Environmental Science

• Identifiers
  DOI 10.1103/PhysRevLett.103.140602arXiv 0907.0921PMID 19905556
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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