Parafermionic observables and their applications to planar statistical physics models

This volume is based on the PhD thesis of the author. Through the examples of the self-avoiding walk, the random-cluster model, the Ising model and others, the book explores in details two important techniques: 1.Discrete holomorphicity and parafermionic observables, which have been used in the past few years to study planar models of statistical physics (in particular their conformal invariance), such as random-cluster models and loop O(n)-models. 2. The Russo-Seymour-Welsh theory for percolation-type models with dependence. This technique was initially available for Bernoulli percolation only. Recently, it has been extended to models with dependence, thus opening the way to a deeper study of their critical regime.