Metastable behavior of stochastic dynamics: A pathwise approach. (English) Zbl 0591.60080

Summary: A new approach to metastability for stochastic dynamics is proposed. The basic idea is to study the statistics of each path, performing time averages along the evolution. Metastability would be characterized by the fact that the process of these time averages converges, under a suitable rescaling, to a measure valued Markov jump process. Here this convergence is shown for the Curie-Weiss mean field dynamics and also for a model with spatial structure: Harris contact process.


60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60J75 Jump processes (MSC2010)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
70F99 Dynamics of a system of particles, including celestial mechanics
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