Reconstructing a Random Potential from its Random Walks

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.

References in corpus (4)

• Force dependent fragility in RNA hairpins
• Inferring DNA sequences from mechanical unzipping: an ideal-case study
• Inferring DNA sequences from mechanical unzipping data: the large-bandwidth case
• Sinai's walk: a statistical aspect

Cited by in corpus (3)

• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Limit laws for transient random walks in random environment on $\z$
• Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing