TY - JOUR
T1 - Metastability for general dynamics with rare transitions : escape time and critical configurations
AU - Cirillo, E.N.M.
AU - Nardi, F.R.
AU - Sohler, J.
PY - 2015
Y1 - 2015
N2 - Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical content, we believe that our results are a useful tool to approach metastability for non-Metropolis systems such as Probabilistic Cellular Automata.
Keywords: Stochastic dynamics Irreversible Markov chains Hitting times Metastability Freidlin Wentzell dynamics
AB - Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical content, we believe that our results are a useful tool to approach metastability for non-Metropolis systems such as Probabilistic Cellular Automata.
Keywords: Stochastic dynamics Irreversible Markov chains Hitting times Metastability Freidlin Wentzell dynamics
U2 - 10.1007/s10955-015-1334-6
DO - 10.1007/s10955-015-1334-6
M3 - Article
SN - 0022-4715
VL - 161
SP - 365
EP - 403
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -