Cut-off and exit from metastability: two sides of the same coin

Olivier Bertoncini, Javiera Barrera M., Roberto Fernández

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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).

Original languageEnglish
Pages (from-to)691-696
Number of pages6
JournalComptes Rendus Mathematique
Issue number11-12
StatePublished - Jun 2008


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