Tail behavior of anisotropic norms for Gaussian random fields

We investigate the logarithmic large deviation asymptotics for anisotropic norms of Gaussian random functions of two variables. The problem is solved by the evaluation of the anisotropic norms of corresponding integral covariance operators. We find the exact values of such norms for some important classes of Gaussian fields. To cite this article: M. Lifshits et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).