Reconstructing a Random Potential from its Random Walks

Simona Cocco (1) , Remi Monasson (2)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

The problem of how many trajectories of a random walker in a potential are needed to reconstruct the values of this potential is studied. We show that this problem can be solved by calculating the probability of survival of an abstract random walker in a partially absorbing potential. The approach is illustrated on the discrete Sinai (random force) model with a drift. We determine the parameter (temperature, duration of each trajectory, ...) values making reconstruction as fast as possible.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Simona Cocco, Remi Monasson. Reconstructing a Random Potential from its Random Walks. EPL - Europhysics Letters, 2008, pp.81, 20002. ⟨hal-00142545⟩