On the number of common sites visited by N random walkers

Abstract

Majumdar and Tamm [Phys. Rev. E 86 021135 (2012), arXiv:1206.6184] recently obtained analytical expressions for the mean number of common sites W_N(t) visited up to time t by N independent random walkers starting from the origin of a d-dimensional lattice. In this short note I show how the different regimes and the corresponding asymptotic power laws can be retrieved using the notion of fractal intersection.

1 page, revtex4-1, logarithmic behavior at the upper critical dimension obtained