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Macroscopic Hausdorff dimension of the level sets of the Airy processes

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arxiv 2501.00772 v2 pith:SNJ5QCHT submitted 2025-01-01 math.PR

Sudeshna Bhattacharjee , Fei Pu This is my paper
classification math.PR
keywords airydimensionhausdorfflevelmacroscopicsetsprobabilitiesprocess
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abstract

We study the Macroscopic Hausdorff dimension of the upper and lower level sets of the Airy processes, following the general method developed in Khoshnevisan et al. \cite{KKX17}. For the Airy$_1$ process, the approach to macroscopic Hausdorff dimension of level sets hinges on some inequalities for its joint probabilities, while for the Airy$_2$ process, we make use of some quantitative estimates on the tail probabilities of its maximum and minimum over an interval.

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