  We study the hole probability of Gaussian random entire functions. More
specifically, we work with the flat model (the zero set of this function has a
distribution which is invariant with respect to the plane isometries). A hole
is the event where the function has no zeros in a disc of radius r. We show
that the logarithm of the probability of the hole event decays asymptotically
like -1/4 * e^2 * r^4 + o(r^4). We also study the behavior of the hole
probability with other types of random coefficients.
