Metastability for general dynamics with rare transitions: escape time and critical configurations. (English) Zbl 1327.82058
Summary: 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.
MSC:
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
Keywords:
stochastic dynamics; irreversible Markov chains; hitting times; metastability; Freidlin Wentzell dynamicsReferences:
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