Limiting eigenvalue distribution of the general deformed Ginibre ensemble
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912560684466176 |
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| author | Sarapin, Roman |
| author_facet | Sarapin, Roman |
| contents | Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. We study the limiting eigenvalue distribution of $X_n$. In arXiv:0807.4898 it was shown that the eigenvalue distribution of $X_n$ converges to some deterministic measure. This measure is known for the case $A_n=0$. Under some general convergence conditions on $A_n$ we prove a formula for the density of the limiting measure. We also obtain an estimation on the rate of convergence of the distribution. The approach used here is based on supersymmetric integration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limiting eigenvalue distribution of the general deformed Ginibre ensemble Sarapin, Roman Mathematical Physics Probability 60B20 Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. We study the limiting eigenvalue distribution of $X_n$. In arXiv:0807.4898 it was shown that the eigenvalue distribution of $X_n$ converges to some deterministic measure. This measure is known for the case $A_n=0$. Under some general convergence conditions on $A_n$ we prove a formula for the density of the limiting measure. We also obtain an estimation on the rate of convergence of the distribution. The approach used here is based on supersymmetric integration. |
| title | Limiting eigenvalue distribution of the general deformed Ginibre ensemble |
| topic | Mathematical Physics Probability 60B20 |
| url | https://arxiv.org/abs/2409.02314 |