Second-quantization approach to characteristic polynomials in RMT

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The distribution of the characteristic polynomial Z(U, theta) of N x N matrices U in the circular unitary ensemble is studied by the method of second quantization for one-dimensional fermions. For infinite N the Gaussian distribution of Z(U, theta) is established straightforwardly by bosonization. A general expression for the n-point correlation function of the characteristic polynomial at different points is given by this method. The case of finite N is discussed.
Original languageEnglish
Pages (from-to)3553-3560
Number of pages8
JournalJournal of Physics A: Mathematical and General
Issue number17
Publication statusPublished - 4 May 2001


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