# Extreme Event Statistics in a Drifting Markov Chain

## TL;DR

This study investigates extreme event statistics in a drifting Markov chain modeled by atomic diffusion, verifying theoretical predictions and demonstrating how small drifts influence rare event distributions, with implications for detecting subtle signals in correlated data.

## Contribution

The paper extends extreme event analysis to Markov chains with drift, verifying the Sparre Andersen theorem applicability and showing how small drifts affect extreme value statistics.

## Key findings

- Extreme value distributions are shaped by the underlying exponential distance distribution.
- Small drifts significantly influence record and extreme event statistics.
- Drift detection can be achieved without detailed knowledge of the underlying distribution.

## Abstract

We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that for our data the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.