Lattice Models

Lecturer: Clément Hongler

Assistant: Laurie Field

This page hosts the exercise sheets and solutions for the Autumn 2016 course “Lattice Models” at EPFL.

On Prof. Hongler's page, you will find the current version of the main lecture notes and additional percolation notes.

Exercise sheets

Sheet 1—Recurrence and transience of simple random walk

Sheet 2—Laplacian and Green's functions

Sheet 3—Discrete Dirichlet and heat equations

Sheet 4—Estimates for discrete harmonic functions

Sheet 5—Dirichlet energy, discrete Beurling estimate

Sheet 6—Loop-erased walk, uniform spanning trees, matrix tree theorem

Sheet 7—Basic properties of percolation

Sheet 8—Critical site percolation on the triangular lattice

Sheet 9—BK inequality; two-arm half-plane exponent

Sheet 10—Ising model, dynamics, FK model and coupling

Sheet 11—More on the Ising and FK model

Sheet 12—Dimers and loop models

Solutions Sheet 1Sheet 2Sheet 3Sheet 4Sheet 5Sheet 6
      Sheet 7Sheet 8Sheet 9Sheet 10Sheet 11Sheet 12