Level Spacings for SL(2,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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Document Details

Document Type
Technical Report
Publication Date
Jan 15, 1997
Accession Number
ADA333519

Entities

People

  • Daniel N. Rockmore
  • John D. Lafferty

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computations
  • Computer Science
  • Crystal Structure
  • Delta Functions
  • Distribution Functions
  • Eigenvalues
  • Fourier Analysis
  • Generators
  • Markov Chains
  • Mathematics
  • Matrix Theory
  • Personality
  • Probability
  • Random Walk
  • Spectra

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.

Technology Areas

  • Space