Bulk Universality for Sparse Complex non-Hermitian Random Matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913976487510016 |
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| author | Osman, Mohammed |
| author_facet | Osman, Mohammed |
| contents | We prove that the local eigenvalue statistics in the bulk for complex random matrices with independent entries whose $r$-th absolute moment decays as $N^{-1-(r-2)ε}$ for some $ε>0$ are universal. This includes sparse matrices whose entries are the product of a Bernouilli random variable with mean $N^{-1+ε}$ and an independent complex-valued random variable. By a standard truncation argument, we can also conclude universality for complex random matrices with $4+ε$ moments. The main ingredient is a sparse multi-resolvent local law for products involving any finite number of resolvents of the Hermitisation and deterministic $2N\times2N$ matrices whose $N\times N$ blocks are multiples of the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bulk Universality for Sparse Complex non-Hermitian Random Matrices Osman, Mohammed Probability Mathematical Physics We prove that the local eigenvalue statistics in the bulk for complex random matrices with independent entries whose $r$-th absolute moment decays as $N^{-1-(r-2)ε}$ for some $ε>0$ are universal. This includes sparse matrices whose entries are the product of a Bernouilli random variable with mean $N^{-1+ε}$ and an independent complex-valued random variable. By a standard truncation argument, we can also conclude universality for complex random matrices with $4+ε$ moments. The main ingredient is a sparse multi-resolvent local law for products involving any finite number of resolvents of the Hermitisation and deterministic $2N\times2N$ matrices whose $N\times N$ blocks are multiples of the identity. |
| title | Bulk Universality for Sparse Complex non-Hermitian Random Matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2508.03631 |