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.
Categories: math.PR