Dear colleagues, I am glad to advertise the following minicourse intended for young researchers, PhD and Master students: LECTURER: Prof. Dr. W.T.F. den Hollander, Leiden University (The Netherlands), and visiting professor from this year both at NETWORKS Research Unit, IMT Lucca as well as at DIMAI , University of Florence. MINICOURSE TITLE: Interacting Particle Systems on Random Graphs LOCATION: IMT School of Advanced Studies Lucca, Piazza San Francesco 19, 55100 Lucca (Italy) PERIOD: 21-23/10/2025 ABSTRACT: The goal of this mini course is to sketch what is known and not known about interacting particle systems on random graphs, highlight the role of sparse versus dense graphs, exhibit the relevant time scales for critical phenomena and identify how these depend on the size of the graph, list some open problems and indicate some lines of future research. After reviewing the generic properties of interacting particle systems on regular lattices, specific models on two classes of random graphs will be considered: Configuration Models and Erdos-Renyi random graphs. The course is organized in three 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 & 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). See https://networks.imtlucca.it/networks-lecture-series for more information. Thanks for sharing with those who might be interested. Luca Avena