Biased random walks on combs

Details Biased random walks on combs Biased random walks on combs

2007-04-02

arxiv.org/abs/0704.0188v2

J. Phys. A: Math. Theor. 40 (2007) 8265-8288.

Physics

Condensed Matter

Other Condensed Matter

minor changes in technical definitions

Scientific paper

10.1088/1751-8113/40/29/005

We develop rigorous, analytic techniques to study the behaviour of biased random walks on combs. This enables us to calculate exactly the spectral dimension of random comb ensembles for any bias scenario in the teeth or spine. Two specific examples of random comb ensembles are discussed; the random comb with nonzero probability of an infinitely long tooth at each vertex on the spine and the random comb with a power law distribution of tooth lengths. We also analyze transport properties along the spine for these probability measures.

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