ON THE EXACT ASYMPTOTICS OF SMALL DEVIATIONS OF L2-NORM FOR SOME GAUSSIAN RANDOM FIELDS.

In this paper we study the asymptotic behavior of the tail probability P(V 2 < r) as r → 0, where the sum V 2 is given by the formula V 2 = a2Σ_i,j≥1(i+β)-2c(j+δ)-2ξ2 _ij. Here {ξij} are independent standard Gaussian random variables, and a > 0, β > -1, δ > -1, c > 1/2, ≠= 1 are some constants. Thus, we study small deviations of the L2-norm of certain two-parameter Gaussian random fields, that have the structure of a tensor product. [ABSTRACT FROM AUTHOR]