by its average is exponentially distributed. We study the scaling behaviour of the exponent as the number of vertices tends to infinity, deriving upper and lower bounds. We also identify a regime for the magnetic field and the pair potential in which the key hypothesis is satisfied. The critical droplets, representing the saddle points for the crossover, have a size that is of the order of the number of vertices. This is because the random graphs generated by the Configuration Model are expander graphs.
address:
- 'Department of Mathematics, Ruhr University Bochum, Universitätsstraße 150, 44780 Bochum, Germany'
- 'Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.'
- 'Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.'
- 'Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.'
author:
- 'S. Dommers'
- 'F. den Hollander'
- 'O. Jovanovski'
- 'F.R. Nardi'
title: Metastability for Glauber dynamics on random graphs
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Introduction and main theorems
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A physical system is in a *metastable state* when it remains locked for a very long time in a phase that is different from the one corresponding to thermodynamic 