Reconstructing a random potential from its random walksS. Cocco1 and R. Monasson2
1 CNRS-Laboratoire de Physique Statistique de l'ENS - 24 rue Lhomond, 75005 Paris, France
2 CNRS-Laboratoire de Physique Théorique de l'ENS - 24 rue Lhomond, 75005 Paris, France
received 11 June 2007; accepted in final form 13 November 2007; published January 2008
published online 10 December 2007
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.
02.30.Zz - Inverse problems.
05.40.Fb - Random walks and Levy flights.
02.50.Tt - Inference methods.
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