Work

Rigidity of the Stochastic Airy Operator

Year: 2022

Type: article

Abstract: We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres [22] for Dirichlet and Robin boundary conditions. This proves the rigidity of the Airy-$\beta $ point process and the soft-edge limit of rank-$1$ perturbations of Gaussian $\beta $-Ensembles for any $\beta>0$ and solves an open problem mentioned in [9]. Our proof uses a combination of the semigroup theory of the stochastic Airy operator and the techniques for studying insertion and deletion tolerance of point processes developed in [24].

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnac265

Authors: Pierre Yves Gaudreau Lamarre, Promit Ghosal, Wenxuan Li, Yuchen Liao

Institutions: University of Chicago, Massachusetts Institute of Technology, University of Warwick

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: G6607841513, Structures and universalities around the Kardar-Parisi-Zhang equation