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DDC: 510 × Subject: extreme value theory ×

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Now showing 1 - 2 of 2
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    The longest excursion of a random interacting polymer
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Köcher, Janine; König, Wolfgang
    We consider a random N-step polymer under the influence of an attractive interaction with the origin and derive a limit law -- after suitable shifting and norming -- for the length of the longest excursion towards the Gumbel distribution. The embodied law of large numbers in particular implies that the longest excursion is of order log N long. The main tools are taken from extreme value theory and renewal theory.
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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).