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Introduction to Matrix Models with Applications

Gernot Akemann - University of Bielefeld, Bielefeld

  After giving a short overview over various applications of random matrices and the different symmetry classes, the eigenvalue representation, Coulomb gas picture and saddle point approximation is discussed briefly. In the 2 main parts that follow first the method of loop equations is presented in detail in the context of the application to 2 D quantum gravity. Second the method of orthogonal polynomials is introduced where eigenvalue correlation functions can be computed at finite matrix size. The map of QCD to a random matrix model is presented and universal microscopic large-N limits are discussed.  
    P. Di Francesco, P. Ginsparg, J. Zinn-Justin,, 2D Gravity and Random Matrices, ArXiv:hep-th/9306153
    J.J.M. Verbaarschot, QCD, Chiral Random Matrix Theory and Integrability, ArXiv:hep-th/0502029
    G. Akemann, J. Baik, P. Di Francesco, The Oxford handbook of random matrix theory, Oxford University Press (2011)
  Lecture notes