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| HAL: hal-00704704, version 1 |
| arXiv: 1206.0949 |
| Detailed view |  Export this paper |
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| On the length of one-dimensional reactive paths |
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| Frédéric Cérou 1Arnaud Guyader 1, 2, 3 |
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| (2012-06-05) |
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| Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin equation for a double well potential. More precisely, we are interested in so-called reactive paths, namely trajectories which leave definitely one well and reach the other one. The aim of this paper is to precisely analyze the distribution of the lengths of reactive paths in the limit of small temperature, and to compare the theoretical results to numerical results obtained by a Monte Carlo method, namely the multi-level splitting approach. |
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| 1: | ASPI (INRIA - IRISA) |
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INRIA – Université de Rennes 1 – Université de Rennes II - Haute Bretagne |
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| 2: | Département Mathématiques appliquées et sciences sociales - Rennes 2 (MASS) |
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Université de Rennes II - Haute Bretagne |
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| 3: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 4: | MICMAC (INRIA Paris - Rocquencourt) |
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Ecole des Ponts ParisTech – INRIA |
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| 5: | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| Processus stochastiques |
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| Subject | : | Mathematics/Probability |
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| Reactive path – Gumbel distribution – h-transform |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1206.0949 |
| hal-00704704, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00704704 | |
| oai:hal.archives-ouvertes.fr:hal-00704704 | |
| From: Tony Lelievre | |
| Submitted on: Wednesday, 6 June 2012 10:00:07 | |
| Updated on: Tuesday, 11 September 2012 11:44:06 | |
