
CMUCS97106
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS97106
Level Spacings for SL(2,p)
John D. Lafferty, Daniel N. Rockmore*
January 1997*
To appear in Emerging Applications of Number Theory,,
The IMA Volumes in Mathematics and its Applications,
Eds.: A. Friedman, W. Miller, Jr., Springer Verlag, 1997.
CMUCS97106.ps
Keywords: Random matrices, Cayley graphs, expander graphs,
spacing distribution, Gaussian ensemble, Wigner surmise
We investigate the eigenvalue spacing distributions for randomly
generated 4regular Cayley graphs on SL_{2} (F_{p})
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
SL_{2} (F_{p}) we consider are the new expander graphs
recently discovered by Y. Shalom.
In addition, we use a Markov chain method to generate random 4regular
graphs, and observe that the average eigenvalue spacings are closely
approximated by the Wigner surmise.
17 pages
*Departments of Mathematics and Computer Science, Dartmouth College,
Hanover, NH 03755
