Random walk on Bethe lattice and hyperbolic geometry

Cecile Monthus 1, Chistophe Texier 2

Journal of Physics A 29 (1996) 2399-2409

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.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud