Stability of Mesoscopic Fluctuations of Orthogonal Polynomial Ensembles Under Sparse Decaying Perturbations
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909344230014976 |
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| author | Ofner, Daniel |
| author_facet | Ofner, Daniel |
| contents | We study the stability of the mesoscopic fluctuations of certain orthogonal polynomial ensembles on the real line utilizing the recurrence relation of the associated orthogonal polynomials. We prove that under a sparse enough decaying perturbation of the recurrence coefficients the limiting distribution is stable. As a corollary we prove a mesoscopic central limit theorem (at any scale) for a family of singular continuous measures on $[-2,2]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Mesoscopic Fluctuations of Orthogonal Polynomial Ensembles Under Sparse Decaying Perturbations Ofner, Daniel Mathematical Physics Probability We study the stability of the mesoscopic fluctuations of certain orthogonal polynomial ensembles on the real line utilizing the recurrence relation of the associated orthogonal polynomials. We prove that under a sparse enough decaying perturbation of the recurrence coefficients the limiting distribution is stable. As a corollary we prove a mesoscopic central limit theorem (at any scale) for a family of singular continuous measures on $[-2,2]$. |
| title | Stability of Mesoscopic Fluctuations of Orthogonal Polynomial Ensembles Under Sparse Decaying Perturbations |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2410.07699 |