title: Phase transitions in the first-passage time of scale-invariant correlated processes.
abstract: A key quantity describing the dynamics of complex systems is the first-passage time (FPT). The statistical properties of FPT depend on the specifics of the underlying system dynamics. We present a unified approach to account for the diversity of statistical behaviors of FPT observed in real-world systems. We find three distinct regimes, separated by two transition points, with fundamentally different behavior for FPT as a function of increasing strength of the correlations in the system dynamics: stretched exponential, power-law, and saturation regimes. In the saturation regime, the average length of FPT diverges proportionally to the system size, with important implications for understanding electronic delocalization in one-dimensional correlated-disordered systems.
authors.affiliation: Departamento de Física Aplicada II, Universidad de Málaga, E-29071 Málaga, Spain.
authors.forename: Concepción
authors.initials: C
authors.lastname: Carretero-Campos
authors.forename: Pedro
authors.initials: P
authors.lastname: Bernaola-Galván
authors.forename: Plamen Ch
authors.initials: PCh
authors.lastname: Ivanov
authors.forename: Pedro
authors.initials: P
authors.lastname: Carpena
mesh_terms: D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D044367:Phase Transition; D013223:Statistics as Topic