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- W4300546395 abstract "We study the maximum of a Gaussian field on $[0,1]^d$ ($d geq 1$) whose correlations decay logarithmically with the distance. Kahane cite{Kah85} introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritical case. Duplantier, Rhodes, Sheffield and Vargas cite{DRSV12a} cite{DRSV12b} extended Kahane's construction to the critical case and established the KPZ formula at criticality. Moreover, they made in cite{DRSV12a} several conjectures on the supercritical case and on the maximum of this Gaussian field. In this paper we resolve Conjecture 12 in cite{DRSV12a}: we establish the convergence in law of the maximum and show that the limit law is the Gumbel distribution convoluted by the limit of the derivative martingale." @default.
- W4300546395 created "2022-10-03" @default.
- W4300546395 creator A5022159613 @default.
- W4300546395 date "2013-07-04" @default.
- W4300546395 modified "2023-10-16" @default.
- W4300546395 title "Maximum of a log-correlated Gaussian field" @default.
- W4300546395 doi "https://doi.org/10.48550/arxiv.1307.1365" @default.
- W4300546395 hasPublicationYear "2013" @default.
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