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. \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.

In the new version, we include the results on the Airy${}_2$ process