Almost sure uniform convergence of a random Gaussian field conditioned on a large linear form to a non random profile

Philippe Mounaix

Statistics & Probability Letters, 2019, vol. 148, issue C, 164-168

Abstract: We investigate the realizations of a random Gaussian field on a finite domain of Rd in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and almost surely to a non random profile depending only on the covariance and the considered linear functional of the field. This is a significant improvement of the weaker L2-convergence in probability previously obtained in the case of conditioning on a large quadratic functional.

Keywords: Gaussian fields; Concentration properties; Extreme theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.01.018

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