论文信息 - Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas

Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas

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.

Elisabetta Scoppola

[1] Fabio Martinelli,et al. On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising model , 1991 .

[2] R. Schonmann,et al. Behavior of droplets for a class of Glauber dynamics at very low temperature , 1992 .

[3] R. Khasminskii. Stochastic Stability of Differential Equations , 1980 .

[4] Elisabetta Scoppola. Renormalization group for Markov chains and application to metastability , 1993 .

[5] R. Kotecḱy,et al. Shapes of growing droplets—A model of escape from a metastable phase , 1994 .

[6] Fabio Martinelli,et al. Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models , 1990 .

[7] Roberto H. Schonmann,et al. Critical droplets and metastability for a Glauber dynamics at very low temperatures , 1991 .

[8] R. Kotecḱy,et al. Droplet dynamics for asymmetric Ising model , 1993 .

[9] Fabio Martinelli,et al. On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium , 1991 .

[10] M. Freidlin,et al. Random Perturbations of Dynamical Systems , 1984 .