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Author: Chiarini, Alberto × Type: Text ×

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    A note on the Greens function for the transient random walk without killing on the half lattice, orthant and strip
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    Extremes of the supercritical Gaussian free field
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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).