Quasi-Deterministic Properties of Random Gaussian Fields Constrained by a Large Quadratic Form

Completing the study initiated by Mounaix and Collet (J Stat Phys 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 L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} and in probability is proved under mild conditions and the resulting quasi-deterministic behavior of the field is given. Applications to a large 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.