<p>I can't give you a comparison of different options but I can at least tell you that I (having that background) really liked <a href="http://www.springer.com/mathematics/probability/book/978-3-540-64902-1">Grimmett's book</a>.</p>

<p>As an aside: would this have been better as a comment?  I was debating with myself and could not decide.</p>

CC BY-SA 2.5
2011-02-28T16:58:40.080Z
It's an answer to the question.
Suresh Venkat
CC BY-SA 2.5
2011-03-01T01:29:03.877Z
And a good book
Peter Shor 
CC BY-SA 2.5
2011-02-28T16:19:52.147Z
2011-02-28T16:19:52.147Z
Per Austrin
<p>I found <a href="http://books.google.com/books?id=bAIM1_EoQu0C&amp;printsec=frontcover&amp;dq=Complexity+christensen&amp;source=bl&amp;ots=yppfJB0iKe&amp;sig=vxWCkaH8PrrOYxYK-Edcdnf8D2E&amp;hl=en&amp;ei=0SZsTbaZCMXZgQfp3eXLCg&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=3&amp;ved=0CCMQ6AEwAg#v=onepage&amp;q&amp;f=false" rel="nofollow">Complexity and Criticality</a> by Christensen and Maloney to be an excellent introduction.  They devote a section to Percolation, another to the Ising model and the third to Self Organized Criticality.</p>

<p>They stress intuition and as such I find it to be an excellent introductory text, though if you want a more technical reference, you should probably look elsewhere.</p>

CC BY-SA 2.5
2011-02-28T22:53:24.653Z
2011-02-28T22:53:24.653Z
user834
<p>Akash mentioned and linked <a href="http://www.cse.iitd.ernet.in/~bagchi/courses/CSL866_07-08/" rel="nofollow">my lecture notes</a>. I wanted to clarify that they are entirely based on a small subset of Grimmett's book but I made some effort to clarify with extra explanations and figures the parts of that book that were most opaque to me. In fact the whole purpose of putting those notes up was to provide an accessible introduction to Percolation. So, if anyone does plan to go through those notes, I would really appreciate feedback so that I can make them better.</p>

<p>I also wanted to add that <a href="http://rads.stackoverflow.com/amzn/click/0521872324" rel="nofollow">Bollobas and Riordan's book</a> is very good. It clarifies and simplifies some of the basic material covered in Grimmett's book. It also discusses concepts like 1-dependent percolation (which, I feel, can be much more useful for computer scientists than independent percolation) and random voronoi percolation, which is a fascinating topic, not least because it is a site percolation model whose critical probability in the plane is 1/2.</p>

CC BY-SA 2.5
2011-03-05T13:49:57.437Z
2011-03-08T05:32:19.077Z
2011-03-08T05:32:19.077Z
Amitabha Bagchi
<p>You could have a look <a href="http://www.cse.iitd.ernet.in/~bagchi/courses/CSL866_07-08/" rel="nofollow">here</a></p>

<p><strong>EDIT</strong> I should have added that these are the lectures by Amitabha Bagchi at IIT Delhi</p>

CC BY-SA 2.5
2011-02-28T20:18:59.173Z
2011-03-02T01:47:17.463Z
2011-03-02T01:47:17.463Z
Akash Kumar
<p>Same disclaimer as <a href="https://cstheory.stackexchange.com/questions/5200/what-is-an-accessible-introduction-to-percolation-theory/5210#5210">Per Austrin's answer</a>, but I really enjoyed the book by <a href="http://rads.stackoverflow.com/amzn/click/0521872324" rel="nofollow noreferrer">Bollobas and Riordan</a> having your background.</p>

CC BY-SA 2.5
2011-02-28T19:59:47.483Z
2011-02-28T19:59:47.483Z
2017-04-13T12:32:28.080Z
arnab
<p>And right on cue, <a href="http://arxiv.org/abs/1102.5761" rel="nofollow">these lecture notes</a> by Garban and Steif showed up on the arxiv. </p>

CC BY-SA 2.5
2011-03-01T06:23:59.160Z
2011-03-01T06:23:59.160Z
Suresh Venkat
<p>Lyons and Peres' "Probability on Trees and Networks" (available <a href="http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html" rel="nofollow">here</a>) has a few nice chapters on percolation (and the whole book is a good recommendation for anyone interested in probability and stochastic processes on graphs).</p>

CC BY-SA 2.5
2011-03-06T09:38:51.217Z
2011-03-06T09:38:51.217Z
Marcin Kotowski
<p>What is the best place to start for someone in Computer Science with a graduate level background in linear algebra, probability theory, and graph theory?</p>

CC BY-SA 2.5
2011-02-28T07:00:35.230Z
Perhaps http://en.wikipedia.org/wiki/Percolation_theory and references at the bottom.
Dave Clarke
CC BY-SA 2.5
2011-03-01T04:12:05.057Z
Thanks everyone for the answers. All references look great!
Delip
CC BY-SA 2.5
2011-03-01T04:26:11.587Z
You should vote them up then :)
Suresh Venkat
CC BY-SA 2.5
2011-03-01T16:01:21.180Z
Debut question. Apparently, I don't have enough reputation to vote!
Delip
<reference-request><graph-theory><percolation>
What is an accessible introduction to Percolation Theory?
Delip
# What is an accessible introduction to Percolation Theory?

(Asked by: username_0 on 2011-02-28)

What is the best place to start for someone in Computer Science with a graduate level background in linear algebra, probability theory, and graph theory?

**Tags:** reference-request, graph-theory, percolation
> **Comments:**
> **username_1**: Perhaps http://en.wikipedia.org/wiki/Percolation_theory and references at the bottom.  
> **username_0**: Thanks everyone for the answers. All references look great!  
> **username_2**: You should vote them up then :)  
> **username_0**: Debut question. Apparently, I don't have enough reputation to vote!  

---

## 7 answers

### Answer by username_3 on 2011-02-28. Score: 9

I can't give you a comparison of different options but I can at least tell you that I (having that background) really liked [Grimmett's book](http://www.springer.com/mathematics/probability/book/978-3-540-64902-1).

As an aside: would this have been better as a comment? I was debating with myself and could not decide.

> **Comments:**
> **username_2**: It's an answer to the question.  
> **username_4**: And a good book  

---

### Answer by username_5 on 2011-02-28. Score: 5

I found [Complexity and Criticality](http://books.google.com/books?id=bAIM1_EoQu0C&printsec=frontcover&dq=Complexity+christensen&source=bl&ots=yppfJB0iKe&sig=vxWCkaH8PrrOYxYK-Edcdnf8D2E&hl=en&ei=0SZsTbaZCMXZgQfp3eXLCg&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCMQ6AEwAg#v=onepage&q&f=false) by Christensen and Maloney to be an excellent introduction. They devote a section to Percolation, another to the Ising model and the third to Self Organized Criticality.

They stress intuition and as such I find it to be an excellent introductory text, though if you want a more technical reference, you should probably look elsewhere.


---

### Answer by username_6 on 2011-03-05. Score: 5

Akash mentioned and linked [my lecture notes](http://www.cse.iitd.ernet.in/~bagchi/courses/CSL866_07-08/). I wanted to clarify that they are entirely based on a small subset of Grimmett's book but I made some effort to clarify with extra explanations and figures the parts of that book that were most opaque to me. In fact the whole purpose of putting those notes up was to provide an accessible introduction to Percolation. So, if anyone does plan to go through those notes, I would really appreciate feedback so that I can make them better.

I also wanted to add that [Bollobas and Riordan's book](http://rads.stackoverflow.com/amzn/click/0521872324) is very good. It clarifies and simplifies some of the basic material covered in Grimmett's book. It also discusses concepts like 1-dependent percolation (which, I feel, can be much more useful for computer scientists than independent percolation) and random voronoi percolation, which is a fascinating topic, not least because it is a site percolation model whose critical probability in the plane is 1/2.


---

### Answer by username_2 on 2011-03-01. Score: 5

And right on cue, [these lecture notes](http://arxiv.org/abs/1102.5761) by Garban and Steif showed up on the arxiv.


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### Answer by username_7 on 2011-02-28. Score: 4

You could have a look [here](http://www.cse.iitd.ernet.in/~bagchi/courses/CSL866_07-08/)

**EDIT** I should have added that these are the lectures by Amitabha Bagchi at IIT Delhi


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### Answer by username_8 on 2011-02-28. Score: 4

Same disclaimer as [Per Austrin's answer](https://cstheory.stackexchange.com/questions/5200/what-is-an-accessible-introduction-to-percolation-theory/5210#5210), but I really enjoyed the book by [Bollobas and Riordan](http://rads.stackoverflow.com/amzn/click/0521872324) having your background.


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### Answer by username_9 on 2011-03-06. Score: 2

Lyons and Peres' "Probability on Trees and Networks" (available [here](http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html)) has a few nice chapters on percolation (and the whole book is a good recommendation for anyone interested in probability and stochastic processes on graphs).


---

