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Introduction to Matrix Models with Applications |
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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. | ||

Bibliography:- 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) |
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Lecture notes |
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