Dynamics of an outlier in the Gaussian Unitary Ensemble
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918202236207104 |
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| author | Mateus, John Téllez, Gabriel van Wijland, Frédéric |
| author_facet | Mateus, John Téllez, Gabriel van Wijland, Frédéric |
| contents | We endow the elements of a random matrix drawn from the Gaussian Unitary Ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the dynamics exactly which gives us a window on the dynamical scaling behavior at and around the Baik-Ben Arous-Péché transition. Amusingly, while the statics is well-known and accessible via the Hikami-Brézin integrals, our approach for the dynamics is explicitly based on the use of orthogonal polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of an outlier in the Gaussian Unitary Ensemble Mateus, John Téllez, Gabriel van Wijland, Frédéric Statistical Mechanics We endow the elements of a random matrix drawn from the Gaussian Unitary Ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the dynamics exactly which gives us a window on the dynamical scaling behavior at and around the Baik-Ben Arous-Péché transition. Amusingly, while the statics is well-known and accessible via the Hikami-Brézin integrals, our approach for the dynamics is explicitly based on the use of orthogonal polynomials. |
| title | Dynamics of an outlier in the Gaussian Unitary Ensemble |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2509.14424 |