Spectral radii of sparse non-Hermitian random matrices
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916502500802560 |
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| author | Han, Hyungwon |
| author_facet | Han, Hyungwon |
| contents | We provide estimates for the spectral radii of an $n\times n$ sparse non-Hermitian random matrix $Z$ with general entries in the regime $p=d/n$ where $0<d<1$ is fixed. Utilizing the structural results of (Łuczak, '90), we show that the spectral radius $ρ(Z)$ is $0$ with probability converging to some nonzero value, and satisfies the inequality $(ϕ(n))^{-1}\leq ρ(Z)\leq ϕ(n)$ in the asymptotic sense for any function $ϕ$ satisfying $\lim_{n\to\infty}ϕ(n)=\infty$ with the remaining probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01086 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral radii of sparse non-Hermitian random matrices Han, Hyungwon Probability Combinatorics We provide estimates for the spectral radii of an $n\times n$ sparse non-Hermitian random matrix $Z$ with general entries in the regime $p=d/n$ where $0<d<1$ is fixed. Utilizing the structural results of (Łuczak, '90), we show that the spectral radius $ρ(Z)$ is $0$ with probability converging to some nonzero value, and satisfies the inequality $(ϕ(n))^{-1}\leq ρ(Z)\leq ϕ(n)$ in the asymptotic sense for any function $ϕ$ satisfying $\lim_{n\to\infty}ϕ(n)=\infty$ with the remaining probability. |
| title | Spectral radii of sparse non-Hermitian random matrices |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2412.01086 |