Abstract
In this paper, 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].
| Original language | English |
|---|---|
| Article number | 2550022 |
| Journal | Random Matrices: Theory and Application |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2026 |
Bibliographical note
Publisher Copyright:© 2026 World Scientific Publishing Company.
Keywords
- Random matrix theory
- determinantal point process
- mesoscopic fluctuations
- orthogonal polynomial ensembles
- orthogonal polynomials
- perturbations
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