Quantum Chaos on Random Cayley Graphs of SL2[Z/pZ]

Igor Rivin, Naser T. Sardari

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)328-341
Number of pages14
JournalExperimental Mathematics
Volume28
Issue number3
DOIs
StatePublished - Jul 3 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Quantum Chaos on Random Cayley Graphs of SL<sub>2</sub>[Z/<sub>p</sub>Z]'. Together they form a unique fingerprint.

Cite this