Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Poster II

DY 26.29: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1A

Universality of spectral correlations by superbosonization and free probability theory — •Stephan Mandt and Martin R. Zirnbauer — Institut für Theoretische Physik, Universität zu Köln, Germany

We sketch a proof of universality of local level correlation functions for non-Gaussian invariant random matrix ensembles, by using a new method based on the superbosonization formula in combination with elements of free probability theory. Superbosonization, a variant of the method of commuting and anticommuting variables, eclipses the traditional Hubbard-Stratonovich transformation in that it is not restricted to Gaussian probability distributions. Here, we consider random matrices H distributed according to a probability measure of the form exp(-N Tr V(H))dH with V being a polynomial. To apply the superbosonization formula, one needs to have control of the Fourier transform of the measure in the limit of infinite matrix size N. We show this Fourier transform to be determined by a key notion in free probability theory: the R-transform of the asymptotic level density.