1999/02/16 by Clément Sire, Clement Sire · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Fractal #Lattice (music) #Mathematical analysis #Mathematics #Multifractal system #Physics #Random walk #Random walker algorithm #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Upper and lower bounds #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.60.1464
published as Phys. Rev. E 60, 1464 (1999). · 21 pages including 3 PS figures. Submitted to Phys. Rev. E
arxiv created 1999/02/16 · openalex publication_date 1999/08/01 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These probabilities do not display any multifractal properties, contrary to previous numerical claims. The explanation for this apparent multifractal behavior is given, and our conclusions are supported by numerical calculations. These exact results are exploited to compute the large time asymptotics of the survival probability (or the density) which is found to decay as exp[-Ct(1/3)ln(2/3)(t)]. An exact lower bound for the density is found to decay in a similar way.