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Maximum and coupling of the sine-Gordon field

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If you have a question about this talk, please contact Perla Sousi.

In recent years the extremal behaviour of log-correlated spatial Gaussian processes has drawn a lot of attention. For the lattice discrete Gaussian free field (DGFF) in d=2 as well as for general log-correlated Gaussian fields, the limiting law of the centred maximum has been identified as a randomly shifted Gumbel distribution.

In this talk I will explain how an analogous result is obtained for the non-Gaussian sine-Gordon field. I will present a strong coupling at all scales of the sine-Gordon field with the Gaussian free field and demonstrate how this can be used to extend existing methods for the maximum of the DGFF . The talk is based on a joint work with R. Bauerschmidt.

This talk is part of the Probability series.

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