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Alessandra Cipriani, Grassmannian calculus for probability (limited edition)
(with exercises by Simone Baldassari)

Lecture 1: a bit of history and motivation. Grassmannian calculus 101.
Lecture 2: Gaussian variables and determinants with Grassmannians.
Lecture 3: trees and forests with Grassmannianians.
Lecture 4: supersymmetry with Grassmannians.

Frank den Hollander, Interacting Particle Systems on Random Graphs
(with exercises by Federico Capannoli)

Lecture 1. Background and motivation for IPS on Zd, d >= 1. From micro to macro: phase transitions and critical phenomena. Key questions.
Lecture 2. SIM: Stochastic Ising Model.
Lecture 3. VM: Voter Model.
Lecture 4. CP: Contact Process.
In Lectures 2-4, IPS on three classes of random graphs are considered:
  • CM: Configuration Model.
  • HER: Homogeneous Erdős-Rényi Random Graph.
  • IER: Inhomogeneous Erdős-Rényi Random Graph.