Year: 2025
Type: article
Abstract: We derive the characteristic function of stochastic functionals of a random walk whose position is reset to the origin at random times drawn from a general probability distribution. We analyze the long-time behavior and obtain the temporal scaling of the first two moments of any stochastic functional of the random walk when the resetting time distribution exhibits a power-law tail. When the resetting times probability density function has finite moments, the probability density of any functional converges to a delta function centered at its mean, indicating an ergodic phase. We explicitly examine the case of the half-occupation time and derive the ergodicity breaking parameter, the first two moments, and the limiting distribution when the resetting time distribution follows a power-law tail, for both Brownian and subdiffusive random walks. We characterize the three different shapes of the limiting distribution as a function of the exponent of the resetting distribution. Our theoretical findings are supported by Monte Carlo simulations, which show excellent agreement with the analytical results.
Source: Physical review. E
DOI: 10.1103/pcm7-bw2y
Authors: Vicenç Méndez, Rosa Flaquer-Galmés
Institution: Universitat Autònoma de Barcelona
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
Award: G1955489565
OpenAlex ID: W4415166240