Electronic Journal of Probability

On Two-Dimensional Random Walk Among Heavy-Tailed Conductances

Jiří Černý

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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.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 10, 293-313.

Accepted: 6 February 2011
First available in Project Euclid: 1 June 2016

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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]

Random walk among random conductances functional limit theorems fractional kinetics trap models

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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

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