The inspection paradox in stochastic resetting

Arnab Pal, Sarah Kostinski, Shlomi Reuveni

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number021001
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number2
DOIs
StatePublished - 14 Jan 2022

Keywords

  • first-passage processes
  • inspection paradox
  • stochastic resetting

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