2018/11/16 by Axel Masó-Puigdellosas, Daniel Campos, Vicenç Méndez · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Acoustics #Computer science #Demography #Diffusion and Search Dynamics #Econometrics #Economics #Financial economics #Geology #Mathematics #Mechanism (biology) #Movement (music) #Physics #Reset (finance) #Residence #Residence time (fluid dynamics) #Sociology #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Subject (documents) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/ab02f3
11 pages, 8 figures. Submitted to Journal of Statistical Mechanics: Theory and Experiment
arxiv created 2018/11/16 · openalex created_date 2018/11/29 · openalex publication_date 2019/03/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
Abstract In this work, we consider stochastic movement with random resets to the origin followed by a random residence time before the motion starts again. First, we study the transport properties of the walker, i.e. we derive an expression for the mean square displacement of the overall process and study its dependence on the statistical properties of the resets and the residence times probability density functions (PDFs) and the type of movement. From this general formula, we see that the inclusion of the residence after the resets is able to induce super-diffusive to sub-diffusive (or diffusive) regimes and it can also make a sub-diffusive walker reach a constant mean square displacement or even collapse. Second, we study how the reset-and-residence mechanism affects the survival probability of different search processes to a given position, showing that the long time behavior of the reset and residence time PDFs determine the existence of the mean first arrival time.