LOGARITHMIC TERMS IN THE SPECTRAL STATISTICS OF BAND RANDOM MATRICES

Authors
CAURIER E RAMANI A GRAMMATICOS B
Citation
E. Caurier et al., LOGARITHMIC TERMS IN THE SPECTRAL STATISTICS OF BAND RANDOM MATRICES, Journal of physics. A, mathematical and general, 26(15), 1993, pp. 3845-3852
Citations number
28
Categorie Soggetti
Physics
Journal title
Journal of physics. A, mathematical and general → ACNP
ISSN journal
03054470
Volume
26
Issue
15
Year of publication
1993
Pages
3845 - 3852
Database
ISI
SICI code
0305-4470(1993)26:15<3845:LTITSS>2.0.ZU;2-D
Abstract
We present a detailed analysis of the nearest-neighbour spacing distri bution (NNSD) for random matrices on which the non-zero elements are c onfined to a band around the diagonal. The vanishing of the remaining elements induces non-analytic (logarithmic) behaviour for the NNSD at very small spacings. A conjecture for the precise behaviour of these l ogarithmic terms is presented and supported by extensive numerical com putations.