2014/05/03 by E. Ben-Naim, E. Ben‐Naim, P. L. Krapivsky
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Brownian motion #Combinatorics #Diffusion #Diffusion and Search Dynamics #Dimension (graph theory) #Exponent #Fick's laws of diffusion #Mathematics #Maxima #Physics #Position (finance) #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math.PR
paper · pdf · doi:10.1103/physrevlett.113.030604
published as Phys. Rev. Lett. 113, 030604 (2014) · 5 pages, 4 figures
arxiv created 2014/05/03 · openalex publication_date 2014/07/17 · arxiv updated 2014/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.