Work

Lévy Diffusion Under Power-Law Stochastic Resetting

Year: 2026

Type: article

Abstract: We investigated the diffusive dynamics of a Lévy walk subject to stochastic resetting through combined numerical and theoretical approaches. Under exponential resetting, the process mean squared displacement (MSD) undergoes a sharp transition from free superdiffusive behavior with exponent γ0 to a steady-state saturation regime. In contrast, power-law resetting with exponent β exhibits three asymptotic MSD regimes: free superdiffusion for β<1, superdiffusive scaling with a linearly β-decreasing exponent for 1<β<γ0+1, and localization characterized by finite steady-state plateaus for β>γ0+1. MSD scaling laws derived via renewal theory-based analysis demonstrate excellent agreement with numerical simulations. These findings offer new insights for optimizing search strategies and controlling transport processes in non-equilibrium environments.

Source: Entropy

DOI: 10.3390/e28010104

Authors: Jianli Liu, Yunyun Li, Fabio Marchesoni

Institutions: Tongji University, Università di Camerino

Language: English

Topic: Diffusion and Search Dynamics

Subfield: Molecular Biology

Field: Biochemistry, Genetics and Molecular Biology

Domain: Life Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China