Accession Number : ADA333519

Title :   Level Spacings for SL(2,p)

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE

Personal Author(s) : Lafferty, John D. ; Rockmore, Daniel N.

PDF Url : ADA333519

Report Date : 15 JAN 1997

Pagination or Media Count : 16

Abstract : We investigate the eigenvalue spacing distributions for randomly generated 4-regular Cayley graphs on SL2(Fp) by numerically calculating their spectra. We present strong evidence that the distributions are Poisson and hence do not follow the Gaussian orthogonal ensemble. Among the Cayley graphs of SL2(Fp) we consider are the new expander graphs recently discovered by Y. Shalom. In addition, we use a Markov chain method to generate random 4-regular graphs and observe that the average eigenvalue spacings are closely approximated by the Wigner surmise.

Descriptors :   *MATRICES(MATHEMATICS), FOURIER TRANSFORMATION, DISTRIBUTION, GRAPHS, EIGENVALUES, MARKOV PROCESSES, FOURIER ANALYSIS, LAPLACE TRANSFORMATION.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE