Interacting Random Systems | Berlin Math Seminars

Interacting Random Systems 📅

Homepage

https://www.wias-berlin.de/research/rgs/fg5/IRS-sem.jsp?s...

Institute

WIAS

Head

Alexander Zass

Usual time

Wednesdays, 11:30 (CET)

Usual venue

Weierstrass Lecture Room (WIAS-405-406)

Number of talks

Random Systems

Wed, 11.06.25 at 11:30

Weierstrass Lectu...

Michiel Renger TU München

Random Systems

Wed, 04.06.25 at 11:30

Weierstrass Lectu...

Elena Pulvirenti TU Delft

Metastability for the Curie–Weiss–Potts model with unbounded random interactions

Abstract.

I will first introduce the model, i.e. a disordered version of the mean-field q-spin Potts model, where the interaction coefficients between spins are general independent random variables. These random variables are chosen to have fixed mean (for simplicity taken to be 1), well defined log-moment generating function and finite variance. I will then present quantitative estimates of metastability in the regime of large number of particles at fixed temperature, when the system evolves according to a Glauber dynamics. This means that the spin configuration is viewed as a Markov chain where spins flip according to Metropolis rates at a fixed inverse temperature. Our main result identifies conditions ensuring that, with high probability, the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. Our proofs use the potential-theoretic approach to metastability in combination with concentration inequalities. Based on a joint work in collaboration with Johan Dubbeldam, Vicente Lenz and Martin Slowik.

Random Systems

Wed, 21.05.25 at 11:30

Weierstrass Lectu...

Adrian Röllin University of Leeds

Centered Subgraph Counts in Dense Random Graphs

Abstract.

Complex networks appear in many fields, from social media to biology, and understanding their structure often boils down to studying how frequently small subgraphs (such as triangles or squares) appear. In this talk, I will introduce the idea of centered subgraph counts: a way of measuring subgraph occurrences that corrects for the dependence that we observe among regular subgraph counts. By focusing on these centered counts, we can describe and quantify the natural 'fluctuations' in dense random networks via tools first developed by Janson and Nowicki in the study of generalised U-statistics in the 90s. I will explain how these theoretical results lead to practical methods for assessing how well a given network fits a chosen statistical model--often referred to as a goodness-of-fit analysis.