Random walk on Bethe lattice and hyperbolic geometry

Details Random walk on Bethe lattice and hyperbolic geometry Random walk on Bethe lattice and hyperbolic geometry

1995-09-12

arxiv.org/abs/cond-mat/9509067v2

Physics

Condensed Matter

12 pages. Revised version (minor changes) to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/29/10/019

We give the exact solution to the problem of a random walk on the Bethe
lattice through a mapping on an asymmetric random walk on the half-line. We
also study the continuous limit of this model, and discuss in detail the
relation between the random walk on the Bethe lattice and Brownian motion on a
space of constant negative curvature.

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