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

2013/04/15 by L Turban, Loic Turban, Turban, Loic
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Classical Physics (physics.class-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech #physics.class-ph

paper · pdf · doi:10.48550/arxiv.1304.4106

11 pages, 4 figures, typos corrected

openalex publication_date 2013/04/15 · arxiv created 2013/05/27 · arxiv updated 2013/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the number of common sites visited by N random walkers
• The Fractal Geometry of Nature

Related

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• I. Territory covered by N random walkers on deterministic fractals. The Sierpinski gasket
• Multiparticle random walks
• II. Territory covered by N random walkers on stochastic fractals. The percolation aggregate
• Number of distinct and common sites visited by N independent random walkers