Random walk on surfaces with hyperbolic cusps

Colin Guillarmou (1) , Laurent Michel (2) , Hans Christianson (3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 Department of Mathematics [MIT]

We consider the operator associated to a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated to this operator and deduce some rate of convergence of the iterated kernel towards its stationary distribution.

Domaines: Théorie spectrale [math.SP]; Probabilités [math.PR]

Colin Guillarmou, Laurent Michel, Hans Christianson. Random walk on surfaces with hyperbolic cusps. Annales de l'Institut Henri Poincare Physique Theorique, 2011, 12, pp.743-775. ⟨10.1007/s00023-011-0085-4⟩. ⟨hal-00483705⟩