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Painlevé Kernels in Hermitian Matrix Models

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Abstract

After reviewing the Hermitian one-matrix model, we will give a brief introduction to the Hermitian two-matrix model and present a summary of some recent results on the asymptotic behavior of the two-matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a 4×4 Riemann–Hilbert problem related to the Painlevé II equation. Also an open problem will be presented.

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Acknowledgements

Research supported by the grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation.

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  1. Department of Mathematics, Royal Institute of Technology (KTH), Lindstedtsvägen 25, 10044, Stockholm, Sweden

    Maurice Duits

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  1. Maurice Duits
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Correspondence to Maurice Duits.

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Communicated by Percy Deift and Alexander Its.

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Duits, M. Painlevé Kernels in Hermitian Matrix Models. Constr Approx 39, 173–196 (2014). https://doi.org/10.1007/s00365-013-9201-7

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  • DOI: https://doi.org/10.1007/s00365-013-9201-7

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