Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum of a log-correlated Gaussian field   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.

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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc