Quasi-deterministic properties of random Gaussian fields constrained by a large quadratic form

Abstract

Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf 143}, 139-147 (2011)], we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large. Concentration in $L^2$ and in probability is proved under mild conditions and the resulting quasi-deterministic behavior of the field is given. Applications to a large {\it local} quadratic form are considered in two specific cases. In particular, the quasi-deterministic structure of a Gaussian random flow with a large local helicity at some given point is determined explicitly.