Cut-off and exit from metastability: two sides of the same coin |
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Institution: | 1. Laboratoire de mathématiques Raphaël-Salem, UMR 6085 CNRS-Université de Rouen, avenue de l''Université, BP 12, 76801 Saint Étienne du Rouvray, France;2. Departamento de Matemática, Universidad Técnica Federico Sta. María, Av. España, 1680 Casilla 110-V, Valparaíso, Chile |
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Abstract: | We present a general framework linking cut-off and exit excursions for birth-and-death processes on a countable alphabet. Under suitable hypotheses, we prove that cut-off convergence towards a (local) equilibrium is accompanied by exponentially distributed out-of-equilibrium excursions. Furthermore, atypical trajectories leading to these excursions and final cut-off trajectories are related by time inversion; in particular their time lengths have identical laws. To cite this article: O. Bertoncini et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). |
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