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arXiv · 1208.0762

Transitions between critical kernels: from the tacnode kernel and critical kernel in the two-matrix model to the Pearcey kernel

Dries Geudens·Lun Zhang
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Abstract

In this paper we study two multicritical correlation kernels and prove that they converge to the Pearcey kernel in a certain double scaling limit. The first kernel appears in a model of non-intersecting Brownian motions at a tacnode. The second arises as a triple scaling limit of the eigenvalue correlation kernel in the Hermitian two-matrix model with quartic/quadratic potentials. The two kernels are different but can be expressed in terms of the same tacnode Riemann-Hilbert problem. The proof is based on a steepest descent analysis of this Riemann-Hilbert problem. A special feature in the analysis is the introduction of an explicit meromorphic function on a Riemann surface with specified sheet structure.

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Dries Geudens, Lun Zhang. 2012-08-03. Transitions between critical kernels: from the tacnode kernel and critical kernel in the two-matrix model to the Pearcey kernel. https://arxiv.org/abs/1208.0762

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