LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

Julien Randon-Furling

(SAMM - Université Paris-1 Panthéon-Sorbonne)                                                                                                                                                                                                    

On the convex hull of certain planar Lévy processes

We present a result that provides insights into the shape of two-dimensional objects (e.g., polymer chains) modeled by the sample paths of stochastic processes like Brownian motion and Lévy flights. This results consists in an exact, universal formula describing the average number of edges on the convex hull of such sample paths. This average number grows relatively slowly (logarithmically) with the duration of the process, and is mostly independent of the specific distribution of the process's increments.

References:

Universality and time-scale invariance for the shape of planar Lévy processes - Phys. Rev. E 89, 052112

 Convex hull of n planar Brownian paths: an exact formula for the average number of edges -J. Phys. A: Math. Theor. 46 015004