Abstract
We first relate the random matrix model to a Fokker-Planck Hamiltonian system, such that the correlation functions of the model are expressed as the vacuum expectation values of equal-time products of density operators. We then analyze the universality of the random matrix model by solving the Focker-Planck Hamiltonian system for large N. We use two equivalent methods to do this, namely the method of relating it to a system of interacting fermions in one space dimension and the method of collective fields for large N matrix quantum mechanics. The final result using both these methods is the same Hamiltonian system of chiral bosons on a circle, which manifestly exhibits the universality of the random matrix model.
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Sakita, B. Random matrices, fermions, collective fields, and universality. Found Phys 27, 1519–1525 (1997). https://doi.org/10.1007/BF02551498
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DOI: https://doi.org/10.1007/BF02551498