The limiting spectral law for sparse iid matrices
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908428398493696 |
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| author | Sah, Ashwin Sahasrabudhe, Julian Sawhney, Mehtaab |
| author_facet | Sah, Ashwin Sahasrabudhe, Julian Sawhney, Mehtaab |
| contents | Let $A$ be an $n\times n$ matrix with iid entries where $A_{ij} \sim \mathrm{Ber}(p)$ is a Bernoulli random variable with parameter $p = d/n$. We show that the empirical measure of the eigenvalues converges, in probability, to a deterministic distribution as $n \rightarrow \infty$. This essentially resolves a long line of work to determine the spectral laws of iid matrices and is the first known example for non-Hermitian random matrices at this level of sparsity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17635 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The limiting spectral law for sparse iid matrices Sah, Ashwin Sahasrabudhe, Julian Sawhney, Mehtaab Probability Combinatorics Let $A$ be an $n\times n$ matrix with iid entries where $A_{ij} \sim \mathrm{Ber}(p)$ is a Bernoulli random variable with parameter $p = d/n$. We show that the empirical measure of the eigenvalues converges, in probability, to a deterministic distribution as $n \rightarrow \infty$. This essentially resolves a long line of work to determine the spectral laws of iid matrices and is the first known example for non-Hermitian random matrices at this level of sparsity. |
| title | The limiting spectral law for sparse iid matrices |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2310.17635 |