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.
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 1
– Sheet 2
– Sheet 3
– Sheet 4
– Sheet 5
– Sheet 6
Sheet 7
– Sheet 8
– Sheet 9
— Sheet 10
— Sheet 11
— Sheet 12