  By random complex zeroes we mean the zero set of a random entire function
whose Taylor coefficients are independent complex-valued Gaussian variables,
and the variance of the k-th coefficient is 1/k!. This zero set is distribution
invariant with respect to isometries of the complex plane. Extending the
previous results of Sodin and Tsirelson, we compute the variance of linear
statistics of random complex zeroes, and find close to optimal conditions on a
test-function that yield asymptotic normality of fluctuations of the
corresponding linear statistics. We also provide examples of test-functions
with abnormal fluctuations of linear statistics.
