Optimization and Growth in First-Passage Resetting - Archive ouverte HAL Access content directly
Journal Articles Journal of Statistical Mechanics: Theory and Experiment Year : 2021

Optimization and Growth in First-Passage Resetting


We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain, first-passage resetting of isotropic diffusion is non-stationary, with the number of resetting events growing with time as $\sqrt{t}$. We calculate the resulting spatial probability distribution of the particle analytically, and also obtain this distribution by a geometric path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting; this scenario is motivated by reliability theory. The goal is to operate a system close to its maximum capacity without experiencing too many breakdowns. However, when a breakdown occurs the system is reset to its minimal operating point. We define and optimize an objective function that maximizes the reward (being close to maximum operation) minus a penalty for each breakdown. We also investigate extensions of this basic model to include delay after each reset and to two dimensions. Finally, we study the growth dynamics of a domain in which the domain boundary recedes by a specified amount whenever the diffusing particle reaches the boundary after which a resetting event occurs. We determine the growth rate of the domain for the semi-infinite line and the finite interval and find a wide range of behaviors that depend on how much the recession occurs when the particle hits the boundary.

Dates and versions

hal-03117919 , version 1 (21-01-2021)



B. de Bruyne, Julien Randon-Furling, S. Redner. Optimization and Growth in First-Passage Resetting. Journal of Statistical Mechanics: Theory and Experiment, 2021, 1, pp.013203. ⟨10.1088/1742-5468/abcd33⟩. ⟨hal-03117919⟩
21 View
0 Download



Gmail Mastodon Facebook X LinkedIn More