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

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.