Metastable states in brownian energy landscape
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 917-934.

Il est bien connu que les marches aléatoires et les diffusions dans un environnement symétrique aléatoire ont un comportement métastable : elles tendent à rester longtemps dans les puits de l’environnement. Dans le cas où l’environnement est un mouvement brownien linéaire, nous étudions le processus des profondeurs des puits consécutifs de profondeur croissante que la dynamique visite. Quand ces profondeurs sont regardées à l’échelle logarithmique, elles forment un processus stationnaire de renouvellement. Nous donnons une description de la structure de ce processus et nous en déduisons le comportement asymptotique presque sûr et les fluctuations de sa densité empirique.

Random walks and diffusions in symmetric random environment are known to exhibit metastable behavior: they tend to stay for long times in wells of the environment. For the case that the environment is a one-dimensional two-sided standard Brownian motion, we study the process of depths of the consecutive wells of increasing depth that the motion visits. When these depths are looked in logarithmic scale, they form a stationary renewal cluster process. We give a description of the structure of this process and derive from it the almost sure limit behavior and the fluctuations of the empirical density of the process.

DOI : 10.1214/14-AIHP616
Mots-clés : diffusion in random environment, brownian motion, excursion theory, renewal cluster process, confluent hypergeometric equation 
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Cheliotis, Dimitris. Metastable states in brownian energy landscape. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 917-934. doi : 10.1214/14-AIHP616. http://www.numdam.org/articles/10.1214/14-AIHP616/

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