Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs

Takashi Kumagai (RIMS, Kyoto)
Ofer Zeitouni (Weizmann Institute)


We provide conditions that ensure that the maximum of the Gaussian free field on a sequence of graphs fluctuates at the same order as the field at the point of maximal standard deviation; under these conditions, the expectation of the maximum is of the same order as the maximal standard deviation. In particular, on a sequence of such graphs the recentered maximum is not tight, similarly to the situation in $\mathbb{Z}$ but in contrast with the situation in $\mathbb{Z}^2$. We show that our conditions cover a large class of "fractal" graphs.

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Pages: 1-12

Publication Date: September 6, 2013

DOI: 10.1214/ECP.v18-2632


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