Brownian motion and entropy growth on irregular surface
C. Chevalier 1, F. Debbasch 11 Université Pierre et Marie Curie-Paris6, UMR 8112, ERGA-LERMA, 3 rue Galilée, 94200 Ivry, France
Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to the test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions, and that this influence typically grows exponentially with time. The corresponding characteristic times are computed and discussed. Conditional entropies and their growth rates are considered too.
AMS subject classifications: 60J65,8J65,60-xx:60Gxx,82Cxx:82C70
Key words: Brownian motion; stochastic processes on manifolds; lateral diffusions
Email: chevalier firstname.lastname@example.org (C. Chevalier), email@example.com (F. Debbasch)