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Sharp convergence of nonlinear functionals of a class of Gaussian random fields

Abstract:

We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in Hairer and Xu (large-scale limit of interface fluctuation models. ArXiv e-prints arXiv:1802.08192, 2018), but with improved estimates. As a consequence, we establish convergence of a class of Gaussian fields composite with more general functions. These bounds and convergences ar...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s40304-018-0162-9

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
Springer Publisher's website
Journal:
Communications in Mathematics and Statistics Journal website
Volume:
6
Issue:
4
Pages:
509-532
Publication date:
2018-11-10
Acceptance date:
2018-10-24
DOI:
EISSN:
2194-671X
ISSN:
2194-6701
Pubs id:
pubs:946775
URN:
uri:54934e09-37ca-41d6-8b13-1918e6c2ce19
UUID:
uuid:54934e09-37ca-41d6-8b13-1918e6c2ce19
Local pid:
pubs:946775

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