2020/06/30 by Asaf Miron · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Psychology · #Attribution #Diffusion and Search Dynamics #Law #License #Lévy flight #Mathematics #Physics #Political science #Psychology #Quantum mechanics #Random walk #Sociology #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Universality (dynamical systems) #cond-mat.mes-hall #cond-mat.stat-mech #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevresearch.2.032042
published in Physical Review Research 2(3) (American Physical Society) · 6 pages with 4 figures and supplemental material
openalex publication_date 2020/08/19 · arxiv created 2020/08/23 · arxiv updated 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Superdiffusion arises when complicated, correlated, and noisy motion at the microscopic scale conspires to yield peculiar dynamics at the macroscopic scale. It ubiquitously appears in a variety of scenarios, spanning a broad range of scientific disciplines. The approach of superdiffusive systems towards their long-time, asymptotic behavior was recently studied using the Lvy walk of order 1 < < 2, revealing a universal transition at the critical c = 3/2. Here, we investigate the origin of this transition and identify two crucial ingredients: a finite velocity which couples the walker's position to time and a corresponding transition in the fluctuations of the number of walks n completed by the walker at time t.