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.
"On Two-Dimensional Random Walk Among Heavy-Tailed Conductances." Electron. J. Probab. 16 293 - 313, 2011. https://doi.org/10.1214/EJP.v16-849