@article{ECP2632,
author = {Takashi Kumagai and Ofer Zeitouni},
title = {Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {18},
year = {2013},
keywords = {Gaussian free field; fractal graphs},
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.
},
pages = {no. 75, 1-12},
issn = {1083-589X},
doi = {10.1214/ECP.v18-2632},
url = {http://ecp.ejpecp.org/article/view/2632}}