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Thermodynamic Limit and Dispersive Regularisation in Matrix Models
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We show that Hermitian matrix models support the occurrence of a new type of phase transition characterised by dispersive regularisation of the order parameter near the critical point. Using the identification of the partition function with a solution of a reduction of the Toda hierarchy, known as Volterra system, we argue that the singularity is resolved by the onset of a multi-dimensional dispersive shock of the order parameter in the space of coupling constants. This analysis explains the origin and mechanism leading to the emergence of chaotic behaviours observed in M^6 matrix models and extends its validity to even nonlinearity of arbitrary order.
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Recursion Coefficients and Krylov Dynamics in Polynomial Random Matrix Models
Recursion coefficients for high-degree asymmetric polynomial random matrix models are computed efficiently via a moment recursion, with large-n asymptotics reproducing Freud's conjecture and transition regions mapped ...
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