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First Order Asymptotics of Matrix Integrals; A Rigorous Approach Towards the Understanding of Matrix Models

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We investigate the large N limit of spectral measures of matrices which relate to the Gibbs measures of a number of statistical mechanical systems on random graphs. These include the Ising and Potts models on random graphs. For most of these models, we prove that the spectral measures converge almost surely and describe their limit via solutions to an Euler equation for isentropic flow with negative pressure p(ρ)=−3−1π2ρ3.

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Authors and Affiliations

  1. Ecole Normale Superieure de Lyon, Unite de Mathematiques pures et appliquees, UMR 5669, 46 Allee d’Italie, 69364, Lyon Cedex 07, France

    Alice Guionnet

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  1. Alice Guionnet
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Communicated by M. Aizenman

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Guionnet, A. First Order Asymptotics of Matrix Integrals; A Rigorous Approach Towards the Understanding of Matrix Models. Commun. Math. Phys. 244, 527–569 (2004). https://doi.org/10.1007/s00220-003-0992-4

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