The Spectral Boundary of Block Structured Random Matrices
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866912322910420992 |
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| author | Patil, Nirbhay Aguirre-Lopez, Fabian Bouchaud, Jean-Philippe |
| author_facet | Patil, Nirbhay Aguirre-Lopez, Fabian Bouchaud, Jean-Philippe |
| contents | Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11149 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Spectral Boundary of Block Structured Random Matrices Patil, Nirbhay Aguirre-Lopez, Fabian Bouchaud, Jean-Philippe Disordered Systems and Neural Networks Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes. |
| title | The Spectral Boundary of Block Structured Random Matrices |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2312.11149 |