Source-linked AI summary
Optimal stochastic restart renders fluctuations in first passage times universal
Shlomi Reuveni
TL;DR
The paper asks whether fluctuations in first-passage times under stochastic restart share a universal property across diverse processes. It analyzes diffusion as an example, proves a general result, interprets it probabilistically, and extends it to restart overheads, finding unity relative fluctuation at optimal restart.
Problem
The exact behavior of optimal restart appeared to depend on fine details of the underlying first-passage process, leaving general statements about optima limited.
Method
The paper analyzes diffusion with stochastic restart, formulates a generic restarted first-passage process, proves the fluctuation result, and generalizes it to restart time overheads.
Results
The relative standard deviation of the first-passage time is exactly unity when the restart rate minimizes the mean first-passage time, for arbitrary first-passage processes.
Takeaways & Limitations
Optimal stochastic restart yields universal first-passage-time fluctuations across diverse processes, with applications discussed for search and single-molecule enzymology.
Takeaways & Limitations
The normalized optimal-time distribution is non-universal and can deviate from exponentiality for s ≫1; restart overheads require a generalized treatment.
Abstract
from arXiv · showhide
Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT) processes seem to have very little in common but it is actually quite the other way around. Here we show that the relative standard deviation associated with the FPT of an optimally restarted process, i.e., one that is restarted at a (non-zero) rate which brings the mean FPT to a minimum, is always unity. We interpret, further generalize, and discuss this finding and the implications arising from it.