Diffusion in one dimensional random medium and hyperbolic brownian motion

Alain Comtet 1, 2, Cecile Monthus 1, 2

Journal of Physics A 29 (1996) 1331-1345

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this relationship and study various distributions using stochastic calculus and functional integration.

  • 1. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud
  • 2. LPTPE,
    Université Paris VI - Pierre et Marie Curie