Mean number of encounters of N random walkers and intersection of strongly anisotropic fractals

Loic Turban

Published 2013-04-15, updated 2013-05-27Version 2

We study the mean number of encounters up to time t, E_N(t), taking place in a subspace with dimension d* of a d-dimensional lattice, for N independent random walkers starting simultaneously from the same origin. E_N is first evaluated analytically in a continuum approximation and numerically through Monte Carlo simulations in one and two dimensions. Then we introduce the notion of the intersection of strongly anisotropic fractals and use it to calculate the long-time behaviour of E_N.