2007/03/09 by Sanjib Sabhapandit · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion #Diffusion and Search Dynamics #Exponential function #Extreme value theory #Front (military) #Gumbel distribution #Mathematical analysis #Mathematics #Meteorology #Physics #Position (finance) #Probability density function #Quantum mechanics #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Tracking (education) #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2007/05/l05002
published as J. Stat. Mech. (2007) L05002 · 4 revtex pages
arxiv created 2007/03/09 · openalex publication_date 2007/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Statistical properties of the front of a semi-infinite system of single-file diffusion (a one-dimensional system where particles cannot pass each other, but in between collisions each one independently exhibits diffusive motion) are investigated. Exact as well as asymptotic results are provided for the probability density function of (a) the front position, (b) the maximum of the front positions, and (c) the first-passage time to a given position. The asymptotic laws for the front position and the maximum front position are found to be governed by Fisher–Tippett–Gumbel extreme value statistics. The asymptotic properties of the first-passage time is dominated by a stretched-exponential tail in the distribution. The farness of the front with the rest of the system is investigated by considering (i) the gap from the front to the closest particle, and (ii) the density profile with respect to the front position, and analytical results are provided for late-time behaviours.