Jean-Christohe Mourrat (Université de Provence)

Titre : Speed of convergence to equilibrium for the environment viewed by a random walker.

Résumé : We consider a continuous-time random walk on Z^d moving among random (symmetric) conductances. A property that proved useful for instance to obtain invariance principles is the ergodicity of the process of the environment viewed by the particle. We will show, provided the conductances are i.i.d. and bounded away from 0, how to quantify the speed of convergence to equilibrium of this process. The method starts with the establishment of a Nash inequality. Two complementary approaches follow, one based on a comparison with the simple random walk, the other consisting in proving that some terms appearing in the Nash inequality do not diverge too fast. The result is an algebraic decay of the variance, valid for a large class of functionals of the environment. This decay has interesting consequences in terms of the random walk itself, giving for instance, under some conditions, an estimate of the difference between the mean square displacement and the limit variance of the walk. (arXiv:0902.0204)



Cyrille Lucas (ENS Paris)

Titre : La loi de l'arcsinus comme loi limite de l'agrégat de diffusion interne engendré par la marche de Sinaï



Gabriel Faraud (Université Paris 13)

Titre : Diffusions in random potential

Résumé : We study a model of diffusion in a brownian potential. This model was firstly introduced by T. Brox (1986) as a continuous time analogue of random walk in random environment. We estimate the deviations of this process above or under its typical behavior. Our results rely on different tools such as a representation introduced by Y. Hu, Z. Shi and M. Yor, Kotani's lemma, introduced at first by K. Kawazu and H. Tanaka (1997), and a decomposition of hitting times developped in a recent article by A. Fribergh, N. Gantert and S. Popov (2008) . Our results are in agreement with their results in the discrete case.



Laurent Tournier (Université Claude Bernard Lyon 1)

Titre : Directional transience of random walks in Dirichlet random environment

Résumé : In the same way that Dirichlet distribution arises in the context of Polya's urn, random walks in Dirichlet environment are related to oriented edge reinforced random walks. In this talk, I shall present a striking stability property of Dirichlet environment under time reversal, and show how it allows to prove directional transience of random walks in such environment on Z^d. This is a joint work with Christophe Sabot.



Alexander Fribergh (Université Claude Bernard Lyon 1)

Titre : Vitesse de la marche aléatoire biaisée sur un cluster de percolation



Omar Boukhadra (Université de Provence)

Titre : Estimées du noyau de la chaleur d'une marche aléatoire avec conductances aléatoires à queues lourdes

Résumé



Julien Poisat (Université Claude Bernard Lyon 1)

Titre : Accrochage de polymère avec désordre faiblement corrélé.

Résumé : on s'intéresse à un modèle de type mécanique statistique modélisant un polymère en interaction avec une interface, et plus particulièrement à son diagramme de phase. Des bornes sur la courbe critique seront données lorsque l'on introduit dans ce modèle un désordre faiblement corrélé.