Macroscopic Hausdorff Dimension of Airy Process Level Sets in Probability Theory
Determines the Barlow-Taylor macroscopic Hausdorff dimension of the upper level sets (tall peaks) and lower level sets (deep valleys) of the Airy1 and Airy2 processes, obtaining 1 minus gamma^(3/2) for peaks and 1 minus gamma^3 for valleys, and thereby establishing their multifractality. Proofs use the association (FKG) property for the Airy1 process and quantitative maximum/minimum tail estimates via exponential last passage percolation for the Airy2 process.
2501.00772
The Airy1 and Airy2 processes are stationary stochastic processes that arise as scaling limits of random-growth models in the KPZ universality class, with finite-dimensional distributions expressed t…