Random walks in random environment: What a single trajectory tells

2003/04/07 by Omer Adelman, Adelman, Omer, Nathanaël Enriquez +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60K37 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Theoretical and Computational Physics #math.PR #msc:60K37 #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.math/0304091

10 pages

arxiv created 2003/04/07 · openalex publication_date 2003/04/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a procedure that determines the law of a random walk in an iid random environment as a function of a single "typical" trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law can be determined. We then show how independent trajectories having the distribution of the original walk can be generated as functions of the single observed trajectory.

Related

• Reconstructing a (recurrent) random environment from a single trajectory of Random Walk in Random Environment with errors
• Reconstructing the environment seen by a RWRE
• Sinai's walk: a statistical aspect
• Quenched small deviation for the trajectory of a random walk with time-inhomogeneous random environment
• A Stationary, Mixing and Perturbative Counterexample to the 0-1-law for Random Walk in Random Environment in Two Dimensions