Weakly universal dynamical correlations between eigenvalues of large random matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908638065459200 |
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| author | Mallick, Kirone Téllez, Gabriel van Wijland, Frédéric |
| author_facet | Mallick, Kirone Téllez, Gabriel van Wijland, Frédéric |
| contents | It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the matrix elements evolve according to a Dyson Brownian motion, dynamical correlations retain a large degree of the universality found at equal times when expressed in terms of the characteristics of some partial differential equation in the complex plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weakly universal dynamical correlations between eigenvalues of large random matrices Mallick, Kirone Téllez, Gabriel van Wijland, Frédéric Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the matrix elements evolve according to a Dyson Brownian motion, dynamical correlations retain a large degree of the universality found at equal times when expressed in terms of the characteristics of some partial differential equation in the complex plane. |
| title | Weakly universal dynamical correlations between eigenvalues of large random matrices |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2511.05727 |