  Following the approach of Bj$\ddot{\text{o}}$rklund and Gorodnik, we have
considered the discrepancy function for lattice point counting on domains that
can be nicely tessellated by the action of a diagonal semigroup. We have shown
that suitably normalized discrepancy functions for lattice point counting on
certain tessellated domains satisfy a non-degenerate central limit theorem.
Furthermore, we have also addressed the same problem for affine and congruence
lattice point counting, proving analogous non-degenerate central limit theorems
for them. The main ingredients of the proofs are the method of cumulants and
quantitative multiple mixing estimates.
