Random walks on combs

Details Random walks on combs Random walks on combs

2005-09-26

arxiv.org/abs/hep-th/0509191v1

J.Phys.A39:1009-1038,2006

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, 4 figures

Scientific paper

10.1088/0305-4470/39/5/002

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

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