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Analytical solution and scaling of fluctuations in complex networks traversed by damped, interacting random walkers
Mehdi Bagheri Hamaneh1, Jonah Haber1, Yi-Kuo Yu1
1National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, 8600 Rockville Pike, Bethesda, Maryland 20894, USA.
Abstract:
A general model for random walks (RWs) on networks is proposed. It incorporates damping and time-dependent links, and it includes standard (undamped, noninteracting) RWs (SRWs), coalescing RWs, and coalescing-branching RWs as special cases. The exact, time-dependent solutions for the average numbers of visits (w) to nodes and their fluctuations (σ2) are given, and the long-term σ-w relation is studied. Although σ ∝ w(1/2) for SRWs, this power law can be fragile when coalescing-branching interaction is present. Damping, however, often strengthens it but with an exponent generally different from 1/2.
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