  We probe the presence of long-range correlations in phase fluctuations by
analyzing the higher-order spectrum of resistance fluctuations in ultra-thin
NbN superconducting films. The non-Gaussian component of resistance
fluctuations is found to be sensitive to film thickness close to the
transition, which allows us to distinguish between mean field and
Berezinskii-Kosterlitz-Thouless (BKT) type superconducting transitions. The
extent of non-Gaussianity was found to be bounded by the BKT and mean field
transition temperatures and depend strongly on the roughness and structural
inhomogeneity of the superconducting films. Our experiment outlines a novel
fluctuation-based kinetic probe in detecting the nature of superconductivity in
disordered low-dimensional materials.
