Universal framework for record ages under restart

TL;DR

This paper introduces a universal framework to analyze record age statistics in stochastic time-series with restarts, applicable to various processes and protocols, revealing how restart influences record creation and system growth.

Contribution

It presents a minimal-assumption, universal framework for record age analysis under restart, extending to non-Markovian protocols and diverse systems.

Findings

Benchmarking on 1D random walks validates the framework.

Derived a universal criterion for restart impact on record ages.

Applied to aggregation-shattering, showing growth rate effects.

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.