SOMMER, JU and TRAUTENBERG, HL (1993) THE EIGENVALUE SPECTRUM OF A LARGE SYMMETRICAL RANDOM-MATRIX WITH EXPONENTIAL DISTRIBUTED ELEMENTS. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 26 (17). pp. 4419-4429. ISSN 0305-4470,
Full text not available from this repository.Abstract
A replica solution for the averaged eigenvalue spectrum of a large symmetric N x N matrix with an exponential distribution p(M(ij)) = (square-root N/M0ij) exp{- square-root N M(ij)/M0ij} (M0ij = M0) of the elements is presented. This problem is reduced to the solution for the averaged eigenvalue spectrum of a homogeneous matrix M0ij = M0 with an added Gaussian random matrix. The main part of the obtained spectral density is the well known semicircular law rho(lambda) = (1/2pi M0(2)) square-root 4M(0)2 - lambda2. In contrast to the Gaussian random matrix an additional second spectral region in the vicinity of M0 square-root N is observed. The analytic result is verified by numerically obtained spectra of such matrices.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/53773 |
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