# Rigidity of the Stochastic Airy Operator

@inproceedings{Lamarre2021RigidityOT, title={Rigidity of the Stochastic Airy Operator}, author={Pierre Yves Gaudreau Lamarre and Promit Ghosal and Wenxuan Li and Yuchen Liao}, year={2021} }

We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres [19] for Dirichlet and Robin boundary conditions. This proves the rigidity of the Airy-β point process and the softedge limit of rank-1 perturbations of Gaussian β-Ensembles for any β > 0, and solves an open problem mentioned in [8]. 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…

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