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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.02068 |
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| _version_ | 1866915828809596928 |
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| author | Imbert, Alexis |
| author_facet | Imbert, Alexis |
| contents | Let $A$ be a permutation invariant random matrix and $B$ another random matrix. We give a quantitative bound on the difference between the diagonal of the resolvent of $A+B$ and the diagonal of the resolvent of the free sum with amalgamation over the diagonal of $A$ and $B$. Moreover, we improve the rate of convergence whenever the matrices $A$ and $B$ are sparse and bounded in operator norm. Doing so, we explicitly construct the free sum over the diagonal of $A$ and $B$ as an adjacency operator of a weighted locally finite graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence rate of the diagonal-valued Cauchy-transform for permutation invariant random matrices Imbert, Alexis Probability Let $A$ be a permutation invariant random matrix and $B$ another random matrix. We give a quantitative bound on the difference between the diagonal of the resolvent of $A+B$ and the diagonal of the resolvent of the free sum with amalgamation over the diagonal of $A$ and $B$. Moreover, we improve the rate of convergence whenever the matrices $A$ and $B$ are sparse and bounded in operator norm. Doing so, we explicitly construct the free sum over the diagonal of $A$ and $B$ as an adjacency operator of a weighted locally finite graph. |
| title | Convergence rate of the diagonal-valued Cauchy-transform for permutation invariant random matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2603.02068 |