SHORT Course: Interacting particle systems on random graphs

Monday 9 Mar 2026, 09:00 → Wednesday 11 Mar 2026, 17:00 Europe/Rome

GSSI

Lecturer
Frank den Hollander

Timetable and workload
Lectures: 8 hours

Course content
The goal of this mini-course is to sketch what is known and not known about interacting particle systems on random graphs. In particular, the mini-course highlights the role of sparse versus dense graphs, exhibits the relevant time scales for critical phenomena and identifies how these depend on the size of the graph, lists some open problems, and indicates some lines of future research. After reviewing the generic properties of interacting particle systems on regular lattice, three specific model on two classes of random graphs will be considered: Configuration random graphs and Erdös--Rényi random graphs.

The course is organized into four lectures:

-Lecture 1. Background and motivation for Interacting Particle Systems on d-dimensional lattices. Phase transitions and critical phenomena. Key questions and core tools.

-Lecture 2. Stochastic Ising Model

-Lecture 3. Voter Model

-Lecture 4. Contact Process.

Reference

F. Capannoli, F. den Hollander, Interacting particle systems on random graphs, Ensaios Mat. 40 (2024) 117--176

https://doi.org/10.21711/217504322024/em402