2018/09/30 by Martin R Evans, Martin R. Evans, Satya N. Majumdar +1 · 119 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Physics and Astronomy · #Bacteriophages and microbial interactions #Diffusion and Search Dynamics #Distribution (mathematics) #Period (music) #Position (finance) #Probability distribution #Refractory (planetary science) #Refractory period #Stationary distribution #Stochastic process #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8121/aaf080
published in Journal of Physics A Mathematical and Theoretical 52(1), 01LT01 (Institute of Physics) · Major revision including amended title. 15 pages 1 figure. Accepted for Journal of Physics A Mathematical and Theoretical Letters
openalex created_date 2018/09/27 · arxiv created 2018/11/13 · openalex publication_date 2018/11/13 · arxiv updated 2019/04/02 · openalex updated_date 2026/08/06
Abstract We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the stationary position distribution and analyse the emergence of a delta peak at the resetting position. In the case of a power–law distribution for the refractory period we find slow relaxation. We generalise our results to the case when the resetting period and the refractory period are correlated, by computing the Laplace transform of the survival probability of the process and the mean first passage time, i.e. the mean time to completion of a task. We also compute exactly the joint distribution of the active and absorption time to a fixed target.