[Cut-off et sortie de la métastabilité : les deux faces de la même pièce]
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.
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.
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@article{CRMATH_2008__346_11-12_691_0,
author = {Bertoncini, Olivier and Barrera M., Javiera and Fern\'andez, Roberto},
title = {Cut-off and exit from metastability: two sides of the same coin},
journal = {Comptes Rendus. Math\'ematique},
pages = {691--696},
publisher = {Elsevier},
volume = {346},
number = {11-12},
year = {2008},
doi = {10.1016/j.crma.2008.04.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.04.007/}
}
TY - JOUR AU - Bertoncini, Olivier AU - Barrera M., Javiera AU - Fernández, Roberto TI - Cut-off and exit from metastability: two sides of the same coin JO - Comptes Rendus. Mathématique PY - 2008 SP - 691 EP - 696 VL - 346 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.04.007/ DO - 10.1016/j.crma.2008.04.007 LA - en ID - CRMATH_2008__346_11-12_691_0 ER -
%0 Journal Article %A Bertoncini, Olivier %A Barrera M., Javiera %A Fernández, Roberto %T Cut-off and exit from metastability: two sides of the same coin %J Comptes Rendus. Mathématique %D 2008 %P 691-696 %V 346 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.04.007/ %R 10.1016/j.crma.2008.04.007 %G en %F CRMATH_2008__346_11-12_691_0
Bertoncini, Olivier; Barrera M., Javiera; Fernández, Roberto. Cut-off and exit from metastability: two sides of the same coin. Comptes Rendus. Mathématique, Tome 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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