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Experimental Mathematics Volume 25, 2016 - Issue 4
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Original Articles

Spectral Experiments+

Igor RivinSchool of Mathematics, University of St. Andrews, Fife, Scotland;Temple University, Philadelphia, PA, USACorrespondence[email protected]
Pages 379-388 | Published online: 30 Mar 2016

References

  • [Akemann et al. 11] Gernot Akemann, Jinho Baik, and Philippe Di Francesco. The Oxford Handbook of Random Matrix Theory. Oxford, UK: Oxford University Press, 2011.
  • [Band et al. 07] Ram Band Idan Oren, and Uzy Smilansky. “Nodal Domains on Graphs—How to Count Them and Why?” arXiv preprint arXiv:0711.3416, 2007.
  • [Dekel et al. 11] Yael Dekel, James R. Lee, and Nathan Linial. “Eigenvectors of Random Graphs: Nodal Domains.” Random Struct. Algorithms, 39:1 (2011), 39–58.
  • [Duchon et al. 04] Philippe Duchon, Philippe Flajolet, Guy Louchard, and Gilles Schaeffer. “Boltzmann Samplers for the Random Generation of Combinatorial Structures.” Comb. Prob. Comput. 13:4–5 (2004), 577–625.
  • [Edelsbrunner 01] Herbert Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge, UK: Cambridge University Press, 2001.
  • [Elon 08] Yehonatan Elon. “Eigenvectors of the Discrete Laplacian on Regular Graphs—A Statistical Approach.” J. Phys. A 41:43 (2008), 435203.
  • [Erdős 09] László Erdős, Benjamin Schlein, and Horng-Tzer Yau. “Semicircle Law on Short Scales and Delocalization of Eigenvectors for Wigner Random Matrices.” Ann. Prob. 37:3 (2009), 815–852.
  • [Le Gall 14] Jean-François Le Gall. “Random Geometry on the Sphere.” arXiv preprint arXiv:1403.7943, 2014.
  • [Jakobson 99] Dmitry Jakobson, Stephen D. Miller, Igor Rivin, and Zeév Rudnick. “Eigenvalue Spacings for Regular Graphs.” In Emerging Applications of Number Theory, pp. 317–327. New York, NY: Springer-Verlag, 1999.
  • [Katz and Sarnak 99] Nicholas M. Katz and Peter Sarnak. Random Matrices, Frobenius Eigenvalues, and Monodromy, Vol. 45 of American Mathematical Society Colloquium Publications. Providence, RI: American Mathematical Society, 1999.
  • [Keating 06] J. P. Keating. “Random Matrices and Number Theory.” In Applications of Random Matrices in Physics, Vol. 221 of NATO Sci. Ser. II Math. Phys. Chem., pp. 1–32. Dordrecht: Springer, 2006.
  • [Lin et al. 13] Yong Lin, Gabor Lippner, Dan Mangoubi, and Shing-Tung Yau. “Nodal Geometry of Graphs on Surfaces.” arXiv preprint arXiv:1307.3226, 2013.
  • [McKay 81] Brendan D. McKay. “The Expected Eigenvalue Distribution of a Large Regular Graph.” Linear Algebra Appl. 40 (1981), 203–216.
  • [Mehta 04] Madan Lal Mehta. Random Matrices, Vol. 142. Amsterdam, Netherlands: Elsevier/Academic Press, 2004.
  • [Oren and Smilansky 10] Idan Oren and Uzy Smilansky. “Trace Formulas and Spectral Statistics for Discrete Laplacians on Regular Graphs (II).” J. Phys. A 43:22 (2010), 225205.
  • [Rivin 94] Igor Rivin. “Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume.” Ann. Math. 139 (1994), 553–580.
  • [Rivin 96] Igor Rivin. “A Characterization of Ideal Polyhedra in Hyperbolic 3-Space.” Ann. Math. 143 (1996), 51–70.
  • [Rivin 03] Igor Rivin. “Combinatorial Optimization in Geometry.” Adv. Appl. Math. 31:1 (2003), 242–271.
  • [Xu and Yau 12] Hao Xu and Shing-Tung Yau. “Nodal Domain and Eigenvalue Multiplicity of Graphs.” J. Comb. 3:4 (2012), 609–622.
  • [Ziegler 95] Günter M. Ziegler. Lectures on Polytopes, Vol. 152. New York, NY: Springer-Verlag, 1995.

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