I am about to finish working through Williams's *Probability With Martingales*. I have studied analysis up to the first five chapters of Folland's text but have not studied any combinatorics yet.


It seems like 'combinatorial' probability topics like percolation, probability on graphs and networks, finite Markov chains and random walks are currently very active and I would like to be able to read the current research in at least some of these areas.


While I can find many interesting texts on Amazon etc. I am not sure how well they reflect current work.


I would greatly appreciate a reading list or learning roadmap for this area.


[I am cross-posting this from [Math.SE](https://math.stackexchange.com/questions/949703/learning-roadmap-combinatorial-probability) where it did not get an answer despite a bounty.]



Learning roadmap: 'combinatorial' probability
Geoffrey Grimmett's *Probability on Graphs* is an excellent introduction to a variety of current active research areas in discrete probability theory, and is probably at about the level you want (you may find that you need to consult other books if there is background you need to fill in, but that isn't a bad thing). It also has quite a number of very stimulating exercises. It's available free from [his web site](http://www.statslab.cam.ac.uk/~grg/books/pgs.html).


