Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15347 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908275467878400 |
|---|---|
| author | Götz, Helene Nagel, Jan |
| author_facet | Götz, Helene Nagel, Jan |
| contents | In this paper, we show limit theorems for the weighted spectral measure of the Laguerre ensemble under a nonstandard scaling, when the parameter grows faster than the matrix size. For this parameter scaling, the limit behavior is similar to the case of the Gaussian ensemble. We show a large deviation principle, moderate deviations and a CLT for the spectral measure. For the moderate deviations and the CLT, we observe a particular dependence on the rate of the parameter and a corrective shift by a signed measure. The proofs are based on the tridiagonal representation of the Laguerre ensemble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonstandard Large and Moderate Deviations for the Laguerre Ensemble Götz, Helene Nagel, Jan Probability 60B20, 60F10, 60F05, 47B36 In this paper, we show limit theorems for the weighted spectral measure of the Laguerre ensemble under a nonstandard scaling, when the parameter grows faster than the matrix size. For this parameter scaling, the limit behavior is similar to the case of the Gaussian ensemble. We show a large deviation principle, moderate deviations and a CLT for the spectral measure. For the moderate deviations and the CLT, we observe a particular dependence on the rate of the parameter and a corrective shift by a signed measure. The proofs are based on the tridiagonal representation of the Laguerre ensemble. |
| title | Nonstandard Large and Moderate Deviations for the Laguerre Ensemble |
| topic | Probability 60B20, 60F10, 60F05, 47B36 |
| url | https://arxiv.org/abs/2503.15347 |