2014/09/05 by Łukasz Kuśmierz, Lukasz Kusmierz, Satya N. Majumdar +3 · 10 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Artificial intelligence #Computer science #Diffusion and Search Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #Order (exchange) #Physics #Statistical physics #Stochastic processes and statistical mechanics #Transition (genetics) #Transition time #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.113.220602
published as Phys. Rev. Lett. 113, 220602 (2014) · 5 pages, 6 figures
arxiv created 2014/09/05 · openalex publication_date 2014/11/26 · arxiv updated 2014/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at x0≥0, where successive jumps are drawn independently from an arbitrary jump distribution f(η). In addition, with a probability 0≤r<1, the position of the searcher is reset to its initial position x0. The efficiency of the search strategy is characterized by the mean time to find the target, i.e., the mean first passage time (MFPT) to the origin. For arbitrary jump distribution f(η), initial position x0 and resetting probability r, we compute analytically the MFPT. For the heavy-tailed Lévy stable jump distribution characterized by the Lévy index 0<μ<2, we show that, for any given x0, the MFPT has a global minimum in the (μ,r) plane at (μ*(x0),r*(x0)). We find a remarkable first-order phase transition as x0 crosses a critical value x0* at which the optimal parameters change discontinuously. Our analytical results are in good agreement with numerical simulations.