Issue
EPL
Volume 81, Number 2, January 2008
Article Number 20002
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/81/20002
Published online 10 December 2007
EPL, 81 (2008) 20002
DOI: 10.1209/0295-5075/81/20002

Reconstructing a random potential from its random walks

S. 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

Abstract
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.

PACS
02.30.Zz - Inverse problems.
05.40.Fb - Random walks and Levy flights.
02.50.Tt - Inference methods.

© EPLA 2008