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Title: | Macroscopic and microscopic (non-)universality of compact support random matrix theory |
Authors: | Akemann, G Vernizzi, G |
Issue 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: | Dept of Mathematics Research Papers Mathematical Sciences |
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Macroscopic and Microscopic.pdf | 226.95 kB | Adobe PDF | View/Open |
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