Abstract
We carry out a numerical study of fluctuations in the spectra of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix theory as we increase the number of vertices. A review of the basic facts on graphs and their spectra is included.
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Jakobson, D., Miller, S.D., Rivin, I., Rudnick, Z. (1999). Eigenvalue Spacings for Regular Graphs. In: Hejhal, D.A., Friedman, J., Gutzwiller, M.C., Odlyzko, A.M. (eds) Emerging Applications of Number Theory. The IMA Volumes in Mathematics and its Applications, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1544-8_12
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DOI: https://doi.org/10.1007/978-1-4612-1544-8_12
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