Metastable Dynamics of Interacting Particle Systems

Title

Metastable Dynamics of Interacting Particle Systems

Subject

Mathematics

Creator

Tim Gunaydin

Date

2024

Contributor

Dr Paul Chleboun

Abstract

We consider a stochastic Ising model evolving according to Glauber dynamics on a complete graph $\G$ with two clusters $\G_1$,$\G_2$. We analyse the metastability of the model and its dependence on the interaction coefficient $J^*$ between vertices $v\in G_1$, $w \in \G_2$. We also investigate the change to dynamics when a positive magnetic field with strength $h$ is introduced. In our study of the metastability we focus on the expected hitting time $\mathbb{E}[\tau^m_s]$. In \cite{Manzo}, the authors show that in the absence of deep cycles, provided we have good control on the typical paths from a $\X_m$, it is possible to derive asymptotic results concerning this value. In addition to asymptotic behaviour, we analyse the dynamics in the $n\to \infty$ limit via large deviation theory. Thus we provide weak convergence results for the Gibbs measure for under the mean-field assumption and identify changes to the dynamics below and above critical temperatures.

Meta Tags

Markov Processes, Interacting Particle Systems, Large Deviation Theory

Files

Collection

Citation

Tim Gunaydin, “Metastable Dynamics of Interacting Particle Systems,” URSS SHOWCASE, accessed November 2, 2024, https://urss.warwick.ac.uk/items/show/698.