Random Graphs, Phase Transitions, and the Gaussian Free Field

The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research:

• Scaling limits of random trees and random graphs (Christina Goldschmidt)
• Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin)

• Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.

  Provides introductory accounts of some of the most active and fascinating areas of research in modern probability theory Contains a thorough introduction to each mini-course that will be of value to both beginners and experts Presents topics of considerable contemporary interest in a careful and clear manner

  Inhalt
  Scaling Limits of Random Trees and Random Graphs (C. Goldschmidt).- Lectures on the Ising and Potts Models on the Hypercubic Lattice (H. Duminil-Copin).- Extrema of the Two-Dimensional Discrete Gaussian Free Field (M. Biskup).