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We give the exact solution to the problem of a random walk on the Bethelattice through a mapping on an asymmetric random walk on the half-line. Wealso study the continuous limit of this model, and discuss in detail therelation between the random walk on the Bethe lattice and Brownian motion on aspace of constant negative curvature.Comment: 12 pages. Revised version (minor changes) to appear in J. Phys.

Random walk on the Bethe lattice and hyperbolic Brownian motion