MCS 591: Statistical Physics and Applications

MCS 591

Spring 2021

Monday, Wednesday, Friday 10:00 - 10:50 am online


Will Perkins

Office: SEO 626

Office Hours: Mondays and Wednesdays 11:00am-12:00pm, or by appointment

Course Information

Main Topics of the Course:

  1. Fundamentals of statistical physics: Gibbs measures, partition functions, correlations, phase transitions
  2. Algorithms for approximatate counting and sampling
  3. Phase coexistence and absence of phase transition
  4. Cluster expansion
  5. Polymer models
  6. Entropy methods
  7. Pirogov-Sinai theory
  8. Applications to extremal and enumerative combinatorics
  9. Algorthms at low temperatures
  10. Spin models on random graphs
  11. Sphere packings and the hard sphere model
  • Jan 11What is statistical physics?

  • Jan 13Gibbs measures and partition functions

  • Jan 15Cumulants and derivatives of log Z

  • Jan 18NO CLASS - MLK Day

  • Jan 20Marginals and correlations

  • Jan 22Dynamics

  • Jan 25Spatial and temporal mixing

  • Jan 27Extremal combintorics for regular graphs

  • Jan 29worksheet

  • Feb 1Entropy method

  • Fev 3Occupancy method

  • Feb 5Linar programming and complemnetary slackness

  • Feb 8Matchings in regular graphs

  • Feb 10Independent sets in triangle-free graphs

  • Feb 12Infinite volume limits and phase transitions

  • Feb 15Dobrushin uniqueness

  • Feb 17Path coupling

  • Feb 19worksheet: independent sets of a given size

  • Feb 22Disagreement percolation

  • Feb 24Lee-Yang theory

  • Feb 26Heilmann-Lieb theorem

  • Mar 1Approximate counting and sampling

  • Mar 3Weitz's correlation decay method

  • Mar 5worksheet

  • Mar 8Computational thresholds (Sly's result)

  • Mar 10Cluster expansion

  • Mar 12Cluster expansion convergence

  • Mar 15Probabilistic consequences of convergence

  • Mar 17Series expansion algoritms

  • Mar 19worksheet

  • Mar 22no class - spring break

  • Mar 24no class - spring break

  • Mar 26no class - spring break

  • Mar 29Abstract polymer models

  • Mar 31Algorithms via polymer models and cluster expansion

  • Apr 2BIS-hard problems on expander graphs

  • Apr 5Independent sets in the hypercube

  • Apr 7Independent sets in the hypercube

  • Apr 9Sapozhenko's Lemma (guest lecture by Aditya Potukuchi)

  • Apr 12Peierls' argument

  • Apr 14Slow mixing and phase coexistence on Zd

  • Apr 16worksheet

  • Apr 19Pirogov-Sinai theory

  • Apr 21Pirogov-Sinai theory

  • Apr 23worksheet

  • Apr 26Random graphs

  • Apr 28Random graphs

  • Apr 30Review