Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.07431 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908444117696512 |
|---|---|
| author | Gu, Yandong |
| author_facet | Gu, Yandong |
| contents | We investigate the edge statistics of singular values for products of independent rectangular complex Ginibre matrices. Building on work \cite{LWW23}, which introduced the depth-to-width ratio (DWR) and established the critical kernel, we show that the DWR acts as a sharp threshold: local statistics exhibit Gaussian fluctuations in the low-DWR regime, while the Airy kernel emerges at the soft edge in the high-DWR regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge statistics for singular values of products of rectangular complex Ginibre matrices Gu, Yandong Probability 60B20 We investigate the edge statistics of singular values for products of independent rectangular complex Ginibre matrices. Building on work \cite{LWW23}, which introduced the depth-to-width ratio (DWR) and established the critical kernel, we show that the DWR acts as a sharp threshold: local statistics exhibit Gaussian fluctuations in the low-DWR regime, while the Airy kernel emerges at the soft edge in the high-DWR regime. |
| title | Edge statistics for singular values of products of rectangular complex Ginibre matrices |
| topic | Probability 60B20 |
| url | https://arxiv.org/abs/2507.07431 |