Diversity of sharp restart

Author:

Eliazar IddoORCID,Reuveni ShlomiORCID

Abstract

Abstract When applied to a stochastic process of interest, a restart protocol alters the overall statistical distribution of the process’ completion time; thus, the completion-time’s mean and randomness change. The explicit effect of restart on the mean is well understood, and it is known that: from a mean perspective, deterministic restart protocols—termed sharp restart—can out-perform any other restart protocol. However, little is known on the explicit effect of restart on randomness. This paper is the second in a duo exploring the effect of sharp restart on randomness: via a Shannon-entropy analysis in the first part, and via a diversity analysis in this part. Specifically, gauging randomness via diversity—a measure that is intimately related to the Renyi entropy—this paper establishes a set of universal criteria that determine: (A) precisely when a sharp-restart protocol decreases/increases the diversity of completion times; (B) the very existence of sharp-restart protocols that decrease/increase the diversity of completion times. Moreover, addressing jointly mean-behavior and randomness, this paper asserts and demonstrates when sharp restart has an aligned effect on the two (decreasing/increasing both), and when the effect is antithetical (decreasing one while increasing the other). The joint mean-diversity results require remarkably little information regarding the (original) statistical distributions of completion times, and are remarkably practical and easy to implement.

Funder

European Research Council

Israel Science Foundation

European Union

Publisher

IOP Publishing

Subject

General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics

Reference80 articles.

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5. First order transition for the optimal search time of Lévy flights with resetting;Kusmierz;Phys. Rev. Lett.,2014

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1. Preface: stochastic resetting—theory and applications;Journal of Physics A: Mathematical and Theoretical;2024-01-25

2. Bernoulli trial under restarts: A comparative study of resetting transitions;Physical Review E;2023-11-21

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