Approximation of plurisubharmonic functions by logarithms of Gaussian analytic functions

Let Ω be a bounded psudoconvex domain in CN. Given continuous plurisubharmonic function u on Ω, we construct a sequence of Gaussian analytic functions fₙ on Ω associated with u such that 1/nlog|fₙ| converges to u in L¹loc(Ω) almost surely, as n→∞. Gaussian analytic function fₙ is constructed by its covariance, or equivalently by its reproducing kernel Hilbert space, which is given by weighed Bergman space with weight e⁻²ⁿᵘ with respect to the Lebesgue measure.