Random walk on a population of random walkers

Details Random walk on a population of random walkers Random walk on a population of random walkers

2007-12-17

arxiv.org/abs/0712.2849v1

J. Phys. A: Math. Theor. 41, 015001 (2008)

Physics

Condensed Matter

Statistical Mechanics

16 pages, 9 figures

Scientific paper

We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered.

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