Large deviations for macroscopic observables of heavy-tailed matrices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914954490150912 |
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| author | Bordenave, Charles Guionnet, Alice Male, Camille |
| author_facet | Bordenave, Charles Guionnet, Alice Male, Camille |
| contents | We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the Lévy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries per row. By representing these matrices as weighted graphs, we derive a large deviations principle for key macroscopic observables. Specifically, we focus on the empirical distribution of eigenvalues, the joint neighborhood distribution, and the joint traffic distribution. As an application, we define a notion of microstates entropy for traffic distributions which is additive for free traffic convolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations for macroscopic observables of heavy-tailed matrices Bordenave, Charles Guionnet, Alice Male, Camille Probability We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the Lévy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries per row. By representing these matrices as weighted graphs, we derive a large deviations principle for key macroscopic observables. Specifically, we focus on the empirical distribution of eigenvalues, the joint neighborhood distribution, and the joint traffic distribution. As an application, we define a notion of microstates entropy for traffic distributions which is additive for free traffic convolution. |
| title | Large deviations for macroscopic observables of heavy-tailed matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2409.14027 |