  Already since the work by Abbe and Rayleigh the difficulty of super
resolution where one wants to recover a collection of point sources from
low-resolved microscopy measurements is thought to be dependent on whether the
distance between the sources is below or above a certain resolution or
diffraction limit. Even though there has been a number of approaches to define
this limit more rigorously, there is still a gap between the situation where
the task is known to be hard and scenarios where the task is provably simpler.
For instance, an interesting approach for the univariate case using the size of
the Cram\'er-Rao lower bound was introduced in a recent work by Ferreira Da
Costa and Mitra. In this paper, we prove their conjecture on the transition
point between good and worse tractability of super resolution and extend it to
higher dimensions. Specifically, the bivariate statistical analysis allows to
link the findings by the Cram\'er-Rao lower bound to the classical Rayleigh
limit.
