Spectral homogenization of reversible random walks on Z^d in a random environment

Daniel Boivin (1) , Jérôme Depauw (2, 3)

1 LM-Brest - Laboratoire de Mathématiques
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
3 FDP - Fédération de recherche Denis Poisson

The first result is a homogenization theorem for the Dirichlet eigenvalues of reversible random walks on Z^d with stationary and uniformly elliptic conductances. It is then used to prove that the CLT holds in μ-almost all environments and to study the law of the exit times. Applications to the almost sure convergence of capacities and currents are given in the last section.

Mots clés: Central limit theorem; Difference operators; Dirichlet eigenvalues; Exit times; Random media

Domaines: Probabilités [math.PR]

Daniel Boivin, Jérôme Depauw. Spectral homogenization of reversible random walks on Z^d in a random environment. Stochastic Processes and their Applications, 2003, 104 (1), pp.29-56. ⟨10.1016/S0304-4149(02)00233-8⟩. ⟨hal-00337065⟩