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.
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.