On the Tail Behavior of Anisotropic Norms for Gaussian Random Fields M.A.Lifshits, A.I.Nazarov and Ya.Yu.Nikitin
We investigate the logarithmic large deviation asymptotics for anisotropic norms of Gaussian random functions of two variables. The problem is solved by evaluation of the anisotropic norm of the corresponding integral covariance operator. We find the exact values of such norms for some important classes of Gaussian fields on the square generalizing and extending the results of Nazarov and Nikitin.
On the Tail Behavior of Anisotropic Norms for Gaussian ...
corresponding integral covariance operator. We find the exact val- ues of such norms for some important classes of Gaussian fields on the square generalizing ...
where d and Ï are some important numeric parameters of the field x and Φ is the distribution function of the standard normal law. We apply this relation to the investigation of the Gaussian measure of large balls in the space lp in order to general
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v2. ãFg,Fgã, where v1 = vol.(SL2(Z)\H) and v2 = vol.(Sp2(Z)\H2). Here ãFg|z=0,Fg|z=0ã denotes the Petersson norm of Fg|z=0 on SL2(Z)\HÃSL2(Z)\H (see section 2 for more details). 2010 Mathematics Subject Classification. Primary 11F11, 11F46;
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