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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/472

Title: Macroscopic and microscopic (non-)universality of compact support random matrix theory
Authors: Akemann, G
Vernizzi, G
Publication Date: 2000
Publisher: Elsevier
Citation: Nucl.Phys. B583: 739-757, 2000
Abstract: A random matrix model with a σ-model like constraint, the restricted trace ensemble (RTE), is solved in the large-n limit. In the macroscopic limit the smooth connected two-point resolvent G(z,w) is found to be non-universal, extending previous results from monomial to arbitrary polynomial potentials. Using loop equation techniques we give a closed though non-universal expression for G(z,w), which extends recursively to all higher k-point resolvents. These findings are in contrast to the usual unconstrained one-matrix model. However, in the microscopic large-n limit, which probes only correlations at distance of the mean level spacing, we are able to show that the constraint does not modify the universal sine-law. In the case of monomial potentials V(M)=M2p, we provide a relation valid for finite-n between the k-point correlation function of the RTE and the unconstrained model. In the microscopic large-n limit they coincide which proves the microscopic universality of RTEs.
URI: http://bura.brunel.ac.uk/handle/2438/472
DOI: http://dx.doi.org/10.1016/S0550-3213(00)00325-4
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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