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

<p>Lectures on the Combinatorics of Free Probability (London Mathematical Society Lecture Note Series): 
<a href="http://rads.stackoverflow.com/amzn/click/0521858526" rel="nofollow">http://www.amazon.com/Lectures-Combinatorics-Probability-Mathematical-Society/dp/0521858526</a></p>

<p>Speicher lectures: <a href="http://www.mast.queensu.ca/~speicher/papers/lectures-IHP.pdf" rel="nofollow">http://www.mast.queensu.ca/~speicher/papers/lectures-IHP.pdf</a></p>

CC BY-SA 3.0
2014-07-21T17:24:07.670Z
URL : http://books.google.com/books?id=zsw_-E-QrOkC&pg=PR7&source=gbs_selected_pages&cad=2#v=onepage&q&f=false
Paul Harrington
CC BY-SA 3.0
2014-07-23T15:33:52.610Z
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
CC BY-SA 3.0
2014-07-21T16:59:26.627Z
2014-07-21T16:59:26.627Z
Paul Harrington
<p>I have vaguely heard of this connection between random matrix theory and graphs (the spectral gap of their laplacians) on compact Riemann surfaces. </p>

<ul>
<li><p>Can someone give a pedagogic reference which helps learn this subject? </p></li>
<li><p>Also is there something called "free probability theory" which is somehow equivalent to random matrix theory? </p></li>
<li><p>Would you call the usual QFT of Hermitian matrices a random matrix theory? </p></li>
</ul>

CC BY-SA 3.0
2014-07-21T06:36:42.427Z
Why has this question been downvoted!?
user6818
CC BY-SA 3.0
2014-07-23T04:21:46.017Z
think its borderline research level. there are large amts of refs easily located. see eg [network solutions](http://www.simonsfoundation.org/mathematics-and-physical-science/network-solutions/?redirect=%252Fmathematics-physical-sciences%252Ffeatured-articles) by Klarreich for a nice pop sci overview incl recent research
vzn
<graph-theory><pr.probability><physics><spectral-graph-theory>
References to learn more about graph laplacian.
user6818
# References to learn more about graph laplacian.

(Asked by: username_0 on 2014-07-20)

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?

**Tags:** graph-theory, pr.probability, physics, spectral-graph-theory

> **Comments:**
> **username_0**: Why has this question been downvoted!?  
> **username_1**: think its borderline research level. there are large amts of refs easily located. see eg [network solutions](http://www.simonsfoundation.org/mathematics-and-physical-science/network-solutions/?redirect=%252Fmathematics-physical-sciences%252Ffeatured-articles) by Klarreich for a nice pop sci overview incl recent research  

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## 1 answers

### Answer by username_2 on 2014-07-21. Score: 1

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](http://rads.stackoverflow.com/amzn/click/0521858526)

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

> **Comments:**
> **username_2**: URL : http://books.google.com/books?id=zsw_-E-QrOkC&pg=PR7&source=gbs_selected_pages&cad=2#v=onepage&q&f=false  
> **username_0**: But do these references build the connection with grpahs on Riemann surfaces? (and may be their Laplacians) I m not able to locate it.  

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