Macroscopic Hausdorff dimension of the level sets of the Airy processes

Sudeshna Bhattacharjee; Fei Pu

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arXiv · 2501.00772

Macroscopic Hausdorff dimension of the level sets of the Airy processes

Sudeshna Bhattacharjee·Fei Pu

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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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Sudeshna Bhattacharjee, Fei Pu. 2025-01-01. Macroscopic Hausdorff dimension of the level sets of the Airy processes. https://arxiv.org/abs/2501.00772

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