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Level Spacings for SL(2,p)

Author: John D Lafferty; Daniel N Rockmore; CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE.
Publisher: Ft. Belvoir Defense Technical Information Center 15 JAN 1997.
Edition/Format:   eBook : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Material Type: Internet resource
Document Type: Internet Resource
All Authors / Contributors: John D Lafferty; Daniel N Rockmore; CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE.
OCLC Number: 227860759
Notes: Prepared in collaboration with Dartmouth College, Dept. of Mathematics and Computer Science, Hanover, NH.
Description: 16 p.

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.

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