Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble

Claeys, Tom;Wang, Dong
(2022) Journal of Statistical Physics — Vol. 188, n° 2, p. art. 11 (2022)

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  • Claeys, Tomorcid-logoUCLouvain
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  • Wang, DongUniversity of Chinese Academy of Sciences
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Abstract
We prove the edge and bulk universality of random Hermitian matrices with equi-spaced external source. One feature of our method is that we use neither a Christoffel-Darboux type formula, nor a double-contour formula, which are standard methods to prove universality results for exactly solvable models. This matrix model is an example of a biorthogonal ensemble, which is a special kind of determinantal point process whose kernel generally does not have a Christoffel-Darboux type formula or double-contour representation. Our methods may showcase how to handle universality problems for biorthogonal ensembles in general.
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Claeys, T., & Wang, D. (2022). Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble. Journal of Statistical Physics, 188(2), art. 11. https://doi.org/10.1007/s10955-022-02937-z (Original work published 2022)