Testing the Leutwyler-Smilga prediction regarding the global topological charge distribution on the lattice

I give a sketch of my recent attempt to test the prediction by Leutwyler and Smilga according to which, for QCD in a finite box with $N_{f} \geq 2$, the combination $x = V \Sigma m$ indicates whether the net topological charge of the gauge background proves relevant ($x \ll 1$) or irrelevant ($x \gg 1$) for physical observables.