Kesten H. Probability on Discrete Structures 2004

Textbook in PDF format

Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery.
The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence
Models of First-Passage Percolation
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures
Random Walks on Finite Groups