For gamma in (0,1), the upper level sets of Airy1 and Airy2 have macroscopic Hausdorff dimension 1 - gamma^(3/2), and the lower level sets have dimension 1 - gamma^3, almost surely.
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Macroscopic Hausdorff dimension of the level sets of the Airy processes
For gamma in (0,1), the upper level sets of Airy1 and Airy2 have macroscopic Hausdorff dimension 1 - gamma^(3/2), and the lower level sets have dimension 1 - gamma^3, almost surely.