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H 1 Quenched invariance principle for random walks among random conductances with stable-like jumps

Auteurs : Kumagai, Takashi (Auteur de la Conférence)
CIRM (Editeur )

Résumé : Consider random conductances that allow long range jumps. In particular we consider conductances $C_{xy} = w_{xy}|x − y|^{−d−\alpha}$ for distinct $x, y \in Z^d$ and $0 < \alpha < 2$, where $\lbrace w_{xy} = w_{yx} : x, y \in Z^d\rbrace$ are non-negative independent random variables with mean 1. We prove that under some moment conditions for $w$, suitably rescaled Markov chains among the random conductances converge to a rotationally symmetric $\alpha$-stable process almost surely w.r.t. the randomness of the environments. The proof is a combination of analytic and probabilistic methods based on the recently established de Giorgi-Nash-Moser theory for processes with long range jumps. If time permits, we also discuss quenched heat kernel estimates as well. This is a joint work with Xin Chen (Shanghai) and Jian Wang (Fuzhou).

Keywords : random conductance model; long range jump; stable-like process; quenched invariance principle

Codes MSC :
60G51 - Processes with independent increments; Lévy processes
60G52 - Stable processes
60J25 - Continuous-time Markov processes on general state spaces
60J75 - Jump processes

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 20/12/2018 Date de captation : 10/12/2018 Collection : Research talks Format : MP4 Durée : 00:53:21 Domaine : Probability & Statistics ; Mathematical Physics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-12-10_kumagai.mp4 Informations sur la rencontre Nom de la rencontre : Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilitésOrganisateurs de la rencontre : Imbert, Cyril ; Mouhot, Clément ; Tristani, IsabelleDates : 10/12/2018 - 14/12/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1862.htmlCitation Data DOI : 10.24350/CIRM.V.19483103 Cite this video as: Kumagai, Takashi (2018). Quenched invariance principle for random walks among random conductances with stable-like jumps. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19483103 URI : http://dx.doi.org/10.24350/CIRM.V.19483103

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Bibliographie

1. Chen, X., Kumagai, T., & Wang, J. (2018). Random Conductance Models with Stable-like Jumps I: Quenched Invariance Principle.〈arXiv:1805.04344〉 - https://arxiv.org/abs/1805.04344

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