Abstract
The paper is a report on results on the long time behavior of Markov chains with finite state spaces and with transition probabilities exponentially small in an external parameter β. A general approach based on renormalization group ideas is presented and discussed in the simple case of reversible Markov chains. Applications are also discussed.
Partially supported by grant SC1-CT91-0695 of the Commission of European Communities.
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References
Freidlin, M. I. and Wentzell, A. D. (1984). Random Perturbations of Dynamical Systems. Springer-Verlag, Berlin.
Has’minskii, R. Z. (1980). Stochastic Stability of Differential Equations. Sijthoff-Noord-hoff.
Kotecky, R. and Olivieri, E. (1992). Droplet dynamics for asymmetric Ising model (to appear).
Kotecky, R. and Olivieri, E. Shapes of growing droplets — a model of escape from a metas table phase (to appear).
Martinelli, F., Olivieri, E., and Scoppola, E. (1991). On the Swendsen and Wang dynamics II: Critical droplets and homogeneous nucleation at low temperature for the 2 dimensional Ising model. Journal of Statistical Physics 62, 135.
Martinelli, F., Olivieri, E., and Scoppola, E. (1990). Metastability and exponential ap¬proach to equilibrium for low temperature stochastic Ising models. Journal of Statistical Physics 61, 1105.
Martinelli, F., Olivieri, E., and Scoppola E. (1991). On the Swendsen and Wang dynamics I: Exponential convergence to equilibrium. Journal of Statistical Physics 62, 117.
Neves, E. J. and Schonmann R. H. (1991). Behaviour of droplets for a class of Glauber dynamics at very low temperatures. Communications in Mathematical Physics 137, 209.
Neves, E. J. and Schonmann, R. H. (1992). Critical droplets and metastability for a class of Glauber dynamics at very low temperatures. Probability Theory and Related Fields 91, 331.
Olivieri, E. and Scoppola, E. (to appear).
Scoppola, E.. Renormalization group for Markov chains and application to metastability. Journal of Statistical Physics (to appear).
Scoppola, E.. Metastability and nucleation for 2-dimensional Ising systems. Physica A (to appear).
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© 1994 Springer Science+Business Media Dordrecht
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Scoppola, E. (1994). Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas. In: Grimmett, G. (eds) Probability and Phase Transition. NATO ASI Series, vol 420. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8326-8_18
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DOI: https://doi.org/10.1007/978-94-015-8326-8_18
Publisher Name: Springer, Dordrecht
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