Universal framework for record ages under restart

Abstract

We propose a universal framework to compute record age statistics of a stochastic time-series that undergoes random restarts. The proposed framework makes minimal assumptions on the underlying process and is furthermore suited to treat generic restart protocols going beyond the Markovian setting. After benchmarking the framework for classical random walks on the $1$D lattice, we derive a universal criterion underpinning the impact of restart on the age of the $n$th record for generic time-series with nearest-neighbor transitions. Crucially, the criterion contains a penalty of order $n$, that puts strong constraints on restart expediting the creation of records, as compared to the simple first-passage completion. The applicability of our approach is further demonstrated on an aggregation-shattering process where we compute the typical growth rates of aggregate sizes. This unified framework paves the way to explore record statistics of time-series under restart in a wide range of complex systems.

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Cited by in corpus (15)

• Rate enhancement of gated drift-diffusion process by optimal resetting
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Record Ages of Scale Invariant non-Markovian Random Walks
• Search with stochastic home-returns can expedite classical first passage under resetting
• Queues with resetting: a perspective
• Target Search Optimization by Threshold Resetting
• Quest for optimal quantum resetting: protocols for a particle on a chain
• Random resetting in search problems
• Continuous Gated First-Passage Processes
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• Universal criterion for selective outcomes under stochastic resetting
• Replicating a renewal process at random times
• Returns to the origin of the Pólya walk with stochastic resetting
• Full Record Statistics of 1d Random Walks