First Passage Under Restart

Abstract

First passage under restart has recently emerged as a conceptual framework suitable for the description of a wide range of phenomena, but the endless variety of ways in which restart mechanisms and first passage processes mix and match hindered the identification of unifying principles and general truths. Hope that these exist came from a recently discovered universality displayed by processes under optimal, constant rate, restart---but extensions and generalizations proved challenging as they marry arbitrarily complex processes and restart mechanisms. To address this challenge, we develop a generic approach to first passage under restart. Key features of diffusion under restart---the ultimate poster boy for this wide and diverse class of problems---are then shown to be completely universal.

References in corpus (7)

• Thermodynamic uncertainty relation for biomolecular processes
• First-passage times in complex scale-invariant media
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic resetting
• Stochastic Search with Poisson and Deterministic Resetting
• Monotonous continuous-time random walks with drift and stochastic reset events
• Universal Bound on the Fano Factor in Enzyme Kinetics

Cited by in corpus (4)

• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Localization transition induced by learning in random searches
• Continuous-time random walks with reset events: Historical background and new perspectives
• Survival probability of stochastic processes beyond persistence exponents