Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry

Details Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry

2006-06-03

arxiv.org/abs/math-ph/0606013v1

J.Phys. A39 (2006) 12327-12342

Physics

Mathematical Physics

19 pages

Scientific paper

10.1088/0305-4470/39/40/003

The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space. This is done for orthogonal, unitary and symplectic symmetry. In the case of unitary symmetry, some explicit results for the correlation functions are derived.

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