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Extremes of Some Gaussian Random Interfaces

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Abstract

In this article we give a general criterion for some dependent Gaussian models to belong to maximal domain of attraction of Gumbel, following an application of the Stein–Chen method studied in Arratia et al. (Ann Probab 17(1):9–25, 1989). We also show the convergence of the associated point process. As an application, we show the conditions are satisfied by some of the well-known supercritical Gaussian interface models, namely, membrane model, massive and massless discrete Gaussian free field, fractional Gaussian free field.

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Acknowledgments

The first author’s research was supported by RTG 1845. The last author’s research was supported by Cumulative Professional Development Allowance from Ministry of Human Resource Development, Government of India, and Department of Science and Technology, Inspire funds. He also acknowledges the hospitality of WIAS Berlin where part of the present work was carried out. The authors would like to thank Noemi Kurt for clarifying us some details of the MM and Ofer Zeitouni for asking a question that led to the draft of the present paper. We thank two anonymous referees for their thorough review and highly appreciate the comments and suggestions which contributed to improving the quality of the publication.

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Authors and Affiliations

  1. Technische Universität, Berlin, Germany

    Alberto Chiarini

  2. Weierstrass Institute, Berlin, Germany

    Alessandra Cipriani

  3. Indian Statistical Institute, Kolkata, India

    Rajat Subhra Hazra

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  1. Alberto Chiarini
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  2. Alessandra Cipriani
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  3. Rajat Subhra Hazra
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Correspondence to Rajat Subhra Hazra.

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Chiarini, A., Cipriani, A. & Hazra, R.S. Extremes of Some Gaussian Random Interfaces. J Stat Phys 165, 521–544 (2016). https://doi.org/10.1007/s10955-016-1634-5

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