2024/03/25 by Roberto Artuso, Artuso, Roberto, Darío Javier Zamora +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Cauchy distribution #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Mathematics #Physics #Quantum mechanics #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Statistics #Universality (dynamical systems)
paper · pdf · doi:10.48550/arxiv.2403.16912
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological and biological problems. A remarkable universal property, involving the average of return times to the boundary, has been theoretically proposed, and experimentally verified in quite different contexts. We discuss here mechanisms that lead to violations of universality, induced by boundary effects. We suggest that our analysis should be relevant where non homogeneity appears in the stationary probability distribution in bounded domain.