“Metastability for the randomly dilute Curie-Weiss model with Glauber dynamics”
Venerdì 22 Maggio 2020, ore 11:00 - Zoom - Saeda Marello (University of Bonn)
The Curie-Weiss model (CW) is a classical model of a ferromagnetic spin system in which all spins interact with each other, namely the interaction graph is complete. The randomly dilute Curie-Weiss model (RDCW) is a generalisation of the CW in which the deterministic interaction between pairs of spins is replaced by iid random coefficients. It can be also viewed as an Ising model on a random graph. We will show results in the case where the interaction coefficients are iid Bernoulli random variables with fixed parameter p, i.e. the interaction graph is an Erdős–Rényi random graph.
After giving an introduction on metastability and on the well known results for the CW, we will focus on how the mean metastable hitting time in the RDCW can be approximated by that of the CW, asymptotically as the system size grows. The main methods we used are potential theoretic approach to metastability and concentration of measure inequalities.
Based on joint work with Anton Bovier and Elena Pulvirenti.