2022, Kemp, Luke, Xu, Chi, Depledge, Joanna, Ebi, Kristie L., Gibbins, Goodwin, Kohler, Timothy A., Rockström, Johan, Scheffer, Marten, Schellnhuber, Hans Joachim, Steffen, Will, Lenton, Timothy M.

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.

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).