Mathematical Physics/Probability Theory
Cut-off and exit from metastability: two sides of the same coin
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 691-696.

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.

Nous présentons un cadre général qui relie cut-off et excursions de sortie pour des processus de naissance et de mort sur un alphabet dénombrable. Sous des hypothèses adaptées, nous montrons que le cut-off vers un équilibre (local) est accompagné par une distribution exponentielle des temps de sortie de l'équilibre. De plus, les trajectoires atypiques menant à ces excursions sont les renversées temporelles de trajectoires de cut-off ; en particulier leurs durées suivent la même loi.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.04.007
Bertoncini, Olivier 1; Barrera M., Javiera 2; Fernández, Roberto 1

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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Bertoncini, Olivier; Barrera M., Javiera; Fernández, Roberto. Cut-off and exit from metastability: two sides of the same coin. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 691-696. doi : 10.1016/j.crma.2008.04.007. http://www.numdam.org/articles/10.1016/j.crma.2008.04.007/

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