Comment on the paper "Exact decay of the persistence probability in the Airy$_1$ process" by Ferrari and Liu

TL;DR

This paper observes a surprising similarity between Ferrari and Liu's persistence probability function for the Airy$_1$ process and a large deviation function for current fluctuations in the TASEP, suggesting a common underlying rare event conditioning.

Contribution

It highlights a novel connection between the persistence probability in the Airy$_1$ process and large deviation functions in TASEP, proposing a shared rare event mechanism.

Findings

Similarity between the persistence probability and large deviation functions.

Potential commonality in conditioning on rare events.

Insight into the behavior of current fluctuations in TASEP.

Abstract

We point out that the non-trivial function obtained by Ferrari and Liu for the persistence probability of the Airy$_1$ process has a strikingly similar form as a large deviation function found earlier by the author for current fluctuations of the totally asymmetric exclusion process with periodic boundaries conditioned on flat initial and final states. A proposed explanation for this observation, which relates similar yet clearly distinct quantities, is that both results pertain to conditioning on the same kind of rare events where a current larger than typical is maintained throughout the system.