On the number of common sites visited by N random walkers

2012/09/12 by L Turban, Turban, L.
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1209.2527

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.

Related

• Number of distinct and common sites visited by N independent random walkers
• Mean number of encounters of N random walkers and intersection of strongly anisotropic fractals
• I. Territory covered by N random walkers on deterministic fractals. The Sierpinski gasket
• Multiparticle random walks
• Full distribution of the number of distinct sites visited by a random walker in dimension d ≥ 2