Inference of a random potential from random walk realizations: Formalism and application to the one-dimensional Sinai model with a drift

We consider the Sinai model, in which a random walker moves in a random quenched potential V, and ask the following questions: 1. how can the quenched potential V be inferred from the observations of one or more realizations of the random motion? 2. how many observations (walks) are required to make...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 197; no. 1; p. 012005
Main Authors Cocco, S, Monasson, R
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.12.2009
Subjects
Inference
Mathematical models
Physics
Quenching
Questions
Random walk
Survival
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Summary:We consider the Sinai model, in which a random walker moves in a random quenched potential V, and ask the following questions: 1. how can the quenched potential V be inferred from the observations of one or more realizations of the random motion? 2. how many observations (walks) are required to make a reliable inference, that is, to be able to distinguish between two similar but distinct potentials, V1 and V2? We show how question 1 can be easily solved within the Bayesian framework. In addition, we show that the answer to question 2 is, in general, intimately connected to the calculation of the survival probability of a fictitious walker in a potential W defined from V1 and V2, with partial absorption at sites where V1 and V2 do not coincide. For the one-dimensional Sinai model, this survival probability can be analytically calculated, in excellent agreement with numerical simulations.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/197/1/012005