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Original Articles

Periodic Walks on Large Regular Graphs and Random Matrix Theory

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REFERENCES

  • [Bass 92] H. Bass. “The Ihara–Selberg Zeta Function of a Tree Lattice.” Internat. J. Math. 3 (1992), 717–797.
  • [Berry 85] M. V. Berry. “Semiclassical Theory of Spectral Rigidity.” Proc. Royal Soc. Lond. A 400 (1985), 229.
  • [Bollobás 85] B. Bollobás. Random Graphs. Academic Press, 1985.
  • [Friedman 08] J. Friedman. A Proof of Alon’s Second Eigenvalue Conjecture and Related Problems, Memoirs of the American Mathematical Society 195. American Mathematical Society, 2008.
  • [Haake 01] F. Haake. Quantum Signatures of Chaos. Springer, 2001.
  • [Hashimoto 89] K. Hashimoto. “Zeta Functions of Finite Graphs and Representations of p-adic Groups.” In Automorphic Forms and Geometry of Arithmetic Varieties, Adv. Stud. Pure Math. 15, pp. 211–280. Academic Press, 1989.
  • [Hoory et al. 06] S. Hoory, N. Linial, and A. Wigderson. “Expander Graphs and Their Applications.” Bulletin (New Series) of the American Mathematical Society 43, (2006), 439–561.
  • [Jacobson et al. 99] D. Jacobson, S. Miller, I. Rivin, and Z. Rudnick. “Eigenvalue Spacings for Regular Graphs.” IMA Vol. Math. Appl. 109 (1999), 317–327.
  • [Janson et al. 00] S. Janson, T. Łuczak, and A. Rucińki. Random Graphs. Wiley, 2000.
  • [Keating and Snaith 00] J. P. Keating and N. C. Snaith. “Random Matrix Theory and ζ(1/2 + it).” Commun. Math. Phys. 214 (2000), 57–89.
  • [Kesten 59] H. Kesten. Symmetric Random Walks on Groups. Trans. Am. Math. Soc. 92 (1959), 336–354.
  • [McKay 81] B. D. McKay. “The Expected Eigenvalue Distribution of a Random Labelled Regular Graph.” Linear Algebr. Appl. 40 (1981), 203–216.
  • [Mnëv 07] P. Mnëv. “Discrete Path Integral Approach to the Selberg Trace Formula for Regular Graphs.” Commun. Math. Phys. 274 (2007), 233–241.
  • [Oren and Smilansky 10] I. Oren and Smilansky, U. “Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II).” J. Phys. A: Math. Theor. 43 (2010), 225205, doi:10.1088/1751-8113/43/22/225205.
  • [Oren et al. 09] I. Oren, A. Godel, and U. Smilansky. “Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (I).” J. Phys. A: Math. Theor. 42 (2009), 415101.
  • [Tracy and Widom 96] C. A. Tracy and H. Widom. “On Orthogonal and Symplectic Matrix Ensembles.” Comm. Math. Phys. 177 (1996), 727–754.
  • [Wormald 81] N. C. Wormald. “The Asymptotic Distribution of Short Cycles in Random Regular Graphs.” J. Combin. Theory, Ser. B 31 (1981), 168–182.

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