2021/02/24 by Daniele Notarmuzi, Claudio Castellano, Alessandro Flammini +2 · 7 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Physics and Astronomy · #Branching process #Computer science #Condensed matter physics #Conductivity #Critical exponent #Criticality #Crossover #Diffusion and Search Dynamics #Directed percolation #Ecosystem dynamics and resilience #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Renormalization group #Scaling #Self-organized criticality #Statistical physics #Stochastic processes and statistical mechanics #Universality (dynamical systems) #physics.soc-ph
paper · pdf · doi:10.1103/physreve.103.l020302
published in Physical review. E 103(2), L020302 (American Physical Society) · 5 pages , 3 figures + Supplemental Material
arxiv created 2021/02/24 · openalex publication_date 2021/02/24 · arxiv updated 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of microscopic events produced by a self-exciting Hawkes process, and leverage a percolation framework to study the formation of macroscopic bursts of activity as a function of the resolution parameter. We find that the very same process may result in different distributions of avalanche size and duration, which are understood in terms of the competition between the 1D percolation and the branching process universality class. Pure regimes for the individual classes are observed at specific values of the resolution parameter corresponding to the critical points of the percolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors is observed in a wide region of the diagram. The hybrid scaling appears to be a likely outcome for an analysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolution parameter.