Invariance principle and heat kernel behaviour for the Random Conductance Model in a degenerate ergodic environment

Date

Dec 18, 2014

Time

2:00 PM - 3:00 PM

Speaker

Dr. Sebastian Andres

Affiliation

Universität Bonn

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. St. Neukamm

Description

In this talk we consider a continuous time random walk /$X$/^on $\mathbb{Z}^d$ in an environment of random conductances taking values in $ [0,\infty)$. We will discuss recent results on a quenched functional central limit theorem for this random walk. Assuming that the law of the conductances is stationary ergodic with respect to space shifts, we present such an invariance principle for $/X$/ under some moment conditions on the environment. Under the same conditions we also obtain Gaussian upper bounds on the heat kernel and a local limit theorem. We also present a parabolic Harnack inequality for non-elliptic operators in the discrete setting of graphs, which is needed for the proof of the local limit theorem. This is joint work with J.-D. Deuschel and M. Slowik.

Links

• Webseite der AG Analysis & Stochastik

Last modified: Oct 20, 2014, 6:35:58 PM