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.