Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilités

Collection Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilités

Organizer(s) Imbert, Cyril ; Mouhot, Clément ; Tristani, Isabelle

Date(s) 10/12/2018 - 14/12/2018

linked URL https://conferences.cirm-math.fr/1862.html

00:00:00 / 00:00:00

1 5

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

By Takashi Kumagai

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).

Information about the video

Date of recording 10/12/2018
Date of publication 20/12/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19483103
Cite this video Kumagai, Takashi (10/12/2018). Quenched invariance principle for random walks among random conductances with stable-like jumps. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19483103
URL https://dx.doi.org/10.24350/CIRM.V.19483103

Domain(s)

Probability

Bibliography

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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