2016, Chiarini, Alberto, Cipriani, Alessandra

In this note we derive an exact formula for the Greens function of the random walk on different subspaces of the discrete lattice (orthants, including the half space, and the strip) without killing on the boundary in terms of the Greens function of the simple random walk on Zd, d ≥ 3.

2015, Chiarini, Alberto, Cipriani, Alessandra, Hazra, Rajat Subhra

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as the field with zero boundary conditions. We show that these results follow from an interesting application of the Stein-Chen method from Arratia et al. (1989).