On the spatial persistence for Airy processes
Patrik L. Ferrari, Ren\'e Frings
TL;DR
This paper derives a formula for the spatial persistence probability of Airy processes and numerically investigates the persistence coefficient for Airy_1, revealing its dependence on the threshold.
Contribution
It provides the first explicit formula for the spatial persistence of Airy processes and numerical analysis of the persistence coefficient.
Findings
Derived a formula for the spatial persistence probability of Airy processes.
Numerically determined the persistence coefficient for Airy_1.
Showed the dependence of the persistence coefficient on the threshold.
Abstract
In this short paper we derive a formula for the spatial persistence probability of the Airy_1 and the Airy_2 processes. We then determine numerically a persistence coefficient for the Airy_1 process and its dependence on the threshold.
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