QUENCHED LARGE DEVIATIONS FOR BROWNIAN MOTION IN A RANDOM POTENTIAL

Daniel Boivin (1) , Thi Thu Hien Lê (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is assumed. The proof is based on a method developed by Sznitman (1994) for Brownian motion among Poissonian potential. In particular, the LDP holds for potentials with polynomially decaying correlations such as the classical potentials studied by L. Pastur (1977) and R. Fukushima (2008) and the potentials recently introduced by H. Lacoin (2012).

Mots clés: Brownian motion; stationary random potential; Lyapunov exponents; shape theorem; large deviations

Domaines: Probabilités [math.PR]

Daniel Boivin, Thi Thu Hien Lê. QUENCHED LARGE DEVIATIONS FOR BROWNIAN MOTION IN A RANDOM POTENTIAL. 2019. ⟨hal-01308838v2⟩