The inspection paradox in stochastic resetting
Open Access
- 14 January 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (2), 021001
- https://doi.org/10.1088/1751-8121/ac3cdf
Abstract
The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun will end before those which have just started. Yet, the inspection paradox teaches us that the converse can also happen when randomness is at play. The paradox comes from probability theory, where it is often illustrated by measuring how long passengers wait upon arriving at a bus stop at a random time. Interestingly, such passengers may on average wait longer than the mean time between bus arrivals—a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this viewpoint, we review the inspection paradox and its origins. The insight gained is then used to explain why, and under which conditions, stochastic resetting expedites the completion of random processes. Importantly, this is done with elementary mathematical tools which help develop a probabilistic intuition for stochastic resetting and how it works. This viewpoint can thus be used as an accessible introduction to the subject.Keywords
Funding Information
- H2020 European Research Council (947731)
- Raymond and Beverly Sackler Center for Computational Molecular and Materials Science
- Azrieli Foundation
- Israeli Science Foundation (394/19)
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