I have vaguely heard of this connection between random matrix theory and graphs (the spectral gap of their laplacians) on compact Riemann surfaces.

• Can someone give a pedagogic reference which helps learn this subject?

• Also is there something called "free probability theory" which is somehow equivalent to random matrix theory?

• Would you call the usual QFT of Hermitian matrices a random matrix theory?

• Why has this question been downvoted!? – user6818 Jul 21 '14 at 6:36
• think its borderline research level. there are large amts of refs easily located. see eg network solutions by Klarreich for a nice pop sci overview incl recent research – vzn Jul 23 '14 at 4:21