2018/09/30 by Wanli Wang, Johannes H. P. Schulz, Weihua Deng +1 · 35 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Combinatorics #Function (biology) #Interval (graph theory) #Large deviations theory #Limiting #Mathematics #Observable #Physics #Power law #Quantum mechanics #Rare events #Rate function #Renewal theory #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.98.042139
published in Physical review. E 98(4) (American Physical Society) · 16 figures
openalex publication_date 2018/10/24 · arxiv created 2018/10/25 · arxiv updated 2018/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered. Here we investigate the large deviations of the number of renewals, the forward and backward recurrence time, the occupation time, and the time interval straddling the observation time. We show how non-normalized densities describe these rare fluctuations, and how moments of certain observables are obtained from these limiting laws. Numerical simulations illustrate our results showing the deviations from arcsine, Dynkin, Darling-Kac, Lévy and Lamperti laws.