Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 10, 293-313.
On Two-Dimensional Random Walk Among Heavy-Tailed Conductances
We consider a random walk among unbounded random conductances on the two-dimensional integer lattice. When the distribution of the conductances has an infinite expectation and a polynomial tail, we show that the scaling limit of this process is the fractional kinetics process. This extends the results of the paper [BC10] where a similar limit statement was proved in dimension larger than two. To make this extension possible, we prove several estimates on the Green function of the process killed on exiting large balls.
Electron. J. Probab., Volume 16 (2011), paper no. 10, 293-313.
Accepted: 6 February 2011
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K37: Processes in random environments 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]
This work is licensed under aCreative Commons Attribution 3.0 License.
Černý, Jiří. On Two-Dimensional Random Walk Among Heavy-Tailed Conductances. Electron. J. Probab. 16 (2011), paper no. 10, 293--313. doi:10.1214/EJP.v16-849. https://projecteuclid.org/euclid.ejp/1464820179