The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929687584833536 |
|---|---|
| author | Dai, Guozheng Song, Zeyan Wang, Hanchao |
| author_facet | Dai, Guozheng Song, Zeyan Wang, Hanchao |
| contents | Let A be an n*n random matrix with mean zero and independent inhomogeneous non-constant subgaussian entries. We get that for any k<c\sqrt{n}, the probability of the matrix has a lower rank than n-k that is sub-exponential. Furthermore, we get a deviation inequality for the singular values of A. This extends earlier results of Rudelson's paper in 2024 by removing the assumption of the identical distribution of the entries across the matrix. Our model covers inhomogeneous matrices, allowing different subgaussian moments for the entries as long as their subgaussian moments have a standard upper bound. In the past advance, the assumption of i.i.d entries was required due to the lack of least common denominators of the non-i.i.d random matrix. We can overcome this problem using a randomized least common denominator (RLCD) from Livshyts in 2021. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices Dai, Guozheng Song, Zeyan Wang, Hanchao Probability Let A be an n*n random matrix with mean zero and independent inhomogeneous non-constant subgaussian entries. We get that for any k<c\sqrt{n}, the probability of the matrix has a lower rank than n-k that is sub-exponential. Furthermore, we get a deviation inequality for the singular values of A. This extends earlier results of Rudelson's paper in 2024 by removing the assumption of the identical distribution of the entries across the matrix. Our model covers inhomogeneous matrices, allowing different subgaussian moments for the entries as long as their subgaussian moments have a standard upper bound. In the past advance, the assumption of i.i.d entries was required due to the lack of least common denominators of the non-i.i.d random matrix. We can overcome this problem using a randomized least common denominator (RLCD) from Livshyts in 2021. |
| title | The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2412.18906 |