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2013 Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs
Takashi Kumagai, Ofer Zeitouni
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Electron. Commun. Probab. 18: 1-12 (2013). DOI: 10.1214/ECP.v18-2632

Abstract

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.<br />

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Takashi Kumagai. Ofer Zeitouni. "Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs." Electron. Commun. Probab. 18 1 - 12, 2013. https://doi.org/10.1214/ECP.v18-2632

Information

Accepted: 6 September 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60136
MathSciNet: MR3109630
Digital Object Identifier: 10.1214/ECP.v18-2632

Subjects:
Primary: 60G15
Secondary: 28A80

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