S Mandt and M R Zirnbauer 2010 J. Phys. A: Math. Theor. 43 025201 doi:10.1088/1751-8113/43/2/025201
S Mandt and M R Zirnbauer
Show affiliationsWe consider unitary ensembles of Hermitian N × N matrices governed by a confining potential NV with analytic and uniformly convex V. From earlier work it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner–Efetov supersymmetry method. This insight leads to a potent new technique for the study of local statistics, e.g. level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.
60B15 Probability measures on groups, Fourier transforms, factorization
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Issue 2 (15 January 2010)
Received 27 August 2009, in final form 8 November 2009
Published 10 December 2009
S Mandt and M R Zirnbauer 2010 J. Phys. A: Math. Theor. 43 025201
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