Probability on Graphs: Random Processes on Graphs and Lattices (Institute of Mathematical Statistics Textbooks)

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

• Probability on Trees and Networks (Cambridge Series in Statistical and Probabilistic Mathematics)
• Computer Age Statistical Inference: Algorithms, Evidence, and Data Science (Institute of Mathematical Statistics Monographs)
• Random Graphs (Cambridge Studies in Advanced Mathematics)
• Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)
• Probability and Stochastics (Graduate Texts in Mathematics, Vol. 261)
• The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization)
• The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (MAA Problem Books)
• Theoretical Statistics: Topics for a Core Course (Springer Texts in Statistics)
• Probability and Random Processes
• Markov Chains and Mixing Times