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

Sylvain Prolhac

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arXiv · 2412.09660

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

Sylvain Prolhac

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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.

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Sylvain Prolhac. 2024-12-12. Comment on the paper "Exact decay of the persistence probability in the Airy$_1$ process" by Ferrari and Liu. https://arxiv.org/abs/2412.09660

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