Fluctuations of recentered maxima of discrete Gaussian Free Fields on a class of recurrent graphs

Takashi Kumagai; Ofer Zeitouni

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arXiv · 1302.2135

Fluctuations of recentered maxima of discrete Gaussian Free Fields on a class of recurrent graphs

Takashi Kumagai·Ofer Zeitouni

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Abstract

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

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Takashi Kumagai, Ofer Zeitouni. 2013-02-08. Fluctuations of recentered maxima of discrete Gaussian Free Fields on a class of recurrent graphs. https://arxiv.org/abs/1302.2135

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