Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.13227 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908296791719936 |
|---|---|
| author | Liu, Dang-Zheng Zhang, Lu |
| author_facet | Liu, Dang-Zheng Zhang, Lu |
| contents | For the complex Ginibre ensemble subjected to an additive perturbation by a deterministic normal matrix $X_0$, we establish that under specific spectral conditions on $X_0$, only two distinct types of local spectral statistics emerge at the spectral edge: GinUE statistics and critical statistics, which respectively correspond to regular and quadratically vanishing spectral points. The critical statistics, as a non-Hermitian analogue of Pearcey statistics in random matrix theory, describes a novel point process on the complex plane. This identifies the third (and likely final) universal statistics in non-Hermitian random matrix theory, after the established GinUE bulk and edge universality classes, and represents the primary achievement of this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13227 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical edge statistics for deformed GinUEs Liu, Dang-Zheng Zhang, Lu Probability 60B20 For the complex Ginibre ensemble subjected to an additive perturbation by a deterministic normal matrix $X_0$, we establish that under specific spectral conditions on $X_0$, only two distinct types of local spectral statistics emerge at the spectral edge: GinUE statistics and critical statistics, which respectively correspond to regular and quadratically vanishing spectral points. The critical statistics, as a non-Hermitian analogue of Pearcey statistics in random matrix theory, describes a novel point process on the complex plane. This identifies the third (and likely final) universal statistics in non-Hermitian random matrix theory, after the established GinUE bulk and edge universality classes, and represents the primary achievement of this paper. |
| title | Critical edge statistics for deformed GinUEs |
| topic | Probability 60B20 |
| url | https://arxiv.org/abs/2311.13227 |