Handbook Article on Applications of Random Matrix Theory to QCD

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In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of QCD. The main focus of this chapter is on the spectral properties of the QCD Dirac operator and relations between chiral Random Matrix Theories and chiral Lagrangians. Both spectra of the anti-hermitian Dirac operator and spectra of the nonhermitian Dirac operator at nonzero chemical potential are discussed.