Interacting Particle Systems: Renormalization and Multi-Scale Analysis

This course is oriented to introduce the audience to a circle of dieas which are basic for very powerful methods, known as block arguments, multi-scale analysis and renormalization transformations. Chapter 1. Two basic examples and some tools 1.1. Introduction 1.2. The percolation model. Some basic facts and tools. 1.2.2. Monotonicity. FKG and BK inequalities 1.2.3. Russo's formula 1.2.4. The supercritical phase 1.3. Oriented percolation 1.4. The Harris contact process. Some pasic facts and tools. Chapter 2. One dimensional contact process: rates of convergence. Chapter 3. Application of dynamical renormalization to percolation. Chapter 4. Half-space percolation and multi-dimensional contact process. Chapter 5. Multi-scale analysis at work.