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

Datum

18.12.2014

Zeit

14:00 - 15:00

Sprecher

Dr. Sebastian Andres

Zugehörigkeit

Universität Bonn

Serie

TUD Mathematik AG Analysis & Stochastik

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. St. Neukamm

Beschreibung

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

Letztmalig verändert: 20.10.2014, 18:35:58