# References to learn more about graph laplacian.

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

## 1 Answer

Suggest these free available resources. Most textbooks on graph theory only glance at "free probability theory".

Lectures on the Combinatorics of Free Probability (London Mathematical Society Lecture Note Series): http://www.amazon.com/Lectures-Combinatorics-Probability-Mathematical-Society/dp/0521858526

Speicher lectures: http://www.mast.queensu.ca/~speicher/papers/lectures-IHP.pdf

• URL : books.google.com/… – Paul Harrington Jul 21 '14 at 17:24
• But do these references build the connection with grpahs on Riemann surfaces? (and may be their Laplacians) I m not able to locate it. – user6818 Jul 23 '14 at 15:33