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

2013/02/08 by Takashi Kumagai, Kumagai, Takashi, Ofer Zeitouni +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1302.2135

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 Z². We show that our conditions cover a large class of "fractal" graphs.

Citations

• Brownian Motion and Harmonic Analysis on Sierpinski Carpets

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