Learning roadmap: 'combinatorial' probability

I would suggest you the following papers:

• "Percolation and disordered systems" by G. Grimmet, 2012 reprint, an interesting paper that integrates a previous book by the same author. Here you can also find the introductory chapter of the original book, which illustrates a number of basic concepts in this context, such as bond percolation, critical phenomenon, site percolation, and so on;

• "Percolation and the Random Cluster Model: Combinatorial and Algorithmic Problems" , another review book by Dominic Welsh that illustrates the basilar concepts of percolation theory in a very clear manner;

• "Percolation theory and network modeling applications in soul physics" by B. Berkowitz and R.P. Ewing, 1998, a relatively old but still valuable and extensive review on the links between percolation theory and network modeling, with a particular focus on the role of these theories in explaining the randomness component of porous media behaviour;

• "Conformal invariance of lattice models" by H. Duminil-Copin and S. Smirnov, 2012, a very high-level review on conformal invariance of the planar Ising model that provides rigorous mathematical details on several interesting topics, including FK percolation (see in particular sections 3 and 8), theory of discrete holomorphic functions, and their applications to planar statistical physics;

• "Stochastics" by H.O. Georgii, 2008, a very comprehensive book on stochastic theories and analyses that includes well-written sections dedicated to Markov chains;

• "Markov chains" by J. Norris, 2008, a very interesting book that deals with this topic from a strictly mathematical point of view;

• "Reversible Markov Chains and Random Walks on Graphs" , an interesting monograph on this topic, collecting many articles written by D. Aldous and J. Allen Fill over different years (recompiled version, 2014).