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Tightness of the recentered maximum of log-correlated Gaussian fields. (English) Zbl 1307.60034
Summary: We consider a family of centered Gaussian fields on the $$d$$-dimensional unit box, whose covariance decreases logarithmically in the distance between points. We prove tightness of the recentered maximum of the Gaussian fields and provide exponentially decaying bounds on the right and left tails. We then apply this result to a version of the two-dimensional continuous Gaussian free field.

##### MSC:
 60G15 Gaussian processes 60G60 Random fields 60G70 Extreme value theory; extremal stochastic processes
##### Keywords:
Gaussian fields; tightness; log-correlation
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