Random Graphs, Phase Transitions, and the Gaussian Free Field

PIMS-CRM Summer School in Probability, Vancouver, Canada, June 5–30, 2017

  • Martin T. Barlow
  • Gordon Slade
Conference proceedings SSPROB 2017

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 304)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Christina Goldschmidt
    Pages 1-33

About these proceedings


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.


scaling limits Ising model Potts model randomness random graphs phase transition continuous distributions random trees SSPROB2017

Editors and affiliations

  1. 1.Department of MathematicsThe University of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsThe University of British ColumbiaVancouverCanada

Bibliographic information