Macroscopic Hausdorff dimension of the level sets of the Airy processes
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. KKX17. For the Airy1 process, the approach to macroscopic Hausdorff dimension of level sets hinges on some inequalities for its joint probabilities, while for the Airy2 process, we make use of some quantitative estimates on the tail probabilities of its maximum and minimum over an interval.
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