@article{e2de51d5186d4c4f8bd1a9ec273b1178,

title = "Quantum Chaos on Random Cayley Graphs of SL2[Z/pZ]",

abstract = "We investigate the statistical behavior of the eigenvalues and diameter of random Cayley graphs of SL2[Z/pZ] as the prime number p goes to infinity. We prove a density theorem for the number of exceptional eigenvalues of random Cayley graphs, i.e., the eigenvalues with absolute value bigger than the optimal spectral bound. Our numerical results suggest that random Cayley graphs of SL2[Z/pZ] and the explicit LPS Ramanujan projective graphs of P1(Z/pZ) have optimal spectral gap and diameter as the prime number p goes to infinity.",

author = "Igor Rivin and Sardari, {Naser T.}",

note = "Funding Information: National Science Foundation under Grant No. DMS-1440140 (1440140) We would like to thank Prof. Sarnak for suggesting this project to us and also his insightful comments on the earlier versions of this work. The computations in this article were performed using the Mathematica system. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140, while the second named author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester. Funding Information: We would like to thank Prof. Sarnak for suggesting this project to us and also his insightful comments on the earlier versions of this work. The computations in this article were performed using the Mathematica system. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140, while the second named author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester. Publisher Copyright: {\textcopyright} 2017, {\textcopyright} 2017 Taylor & Francis Group, LLC.",

year = "2019",

month = jul,

day = "3",

doi = "10.1080/10586458.2017.1403982",

language = "English (US)",

volume = "28",

pages = "328--341",

journal = "Experimental Mathematics",

issn = "1058-6458",

publisher = "A K Peters",

number = "3",

}