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Rigidity of the stochastic airy operator
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Gaudreau Lamarre, Pierre Yves, Ghosal, Promit, Li, Wenxuan and Liao, Yuchen (2022) Rigidity of the stochastic airy operator. International Mathematics Research Notices . rnac265. doi:10.1093/imrn/rnac265 ISSN 1073-7928. (In Press)
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Official URL: https://doi.org/10.1093/imrn/rnac265
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].
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| SWORD Depositor: | Library Publications Router | |||||||||
| Library of Congress Subject Headings (LCSH): | Schrödinger operator , Probabilities , Random matrices | |||||||||
| Journal or Publication Title: | International Mathematics Research Notices | |||||||||
| Publisher: | Oxford University Press | |||||||||
| ISSN: | 1073-7928 | |||||||||
| Official Date: | 2022 | |||||||||
| Dates: |
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| Article Number: | rnac265 | |||||||||
| DOI: | 10.1093/imrn/rnac265 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
| Reuse Statement (publisher, data, author rights): | ** Article version: VoR ** From Crossref journal articles via Jisc Publications Router ** History: epub 20-09-2022; issued 20-09-2022. ** Licence for VoR version of this article starting on 20-09-2022: https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Copyright Holders: | © The Author(s) 2022. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com. | |||||||||
| Date of first compliant deposit: | 14 October 2022 | |||||||||
| Date of first compliant Open Access: | 20 September 2023 | |||||||||
| RIOXX Funder/Project Grant: |
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