  In this paper the fundamental parameters of high-$T_c$ superconductivity are
shown to be connected to the statistics of pairons (hole pairs in their
antiferromagnetic environment) on a square lattice. In particular, we study the
density fluctuations and the distribution of the area surrounding each pairon
on the scale of the antiferromagnetic correlation length $\xi_{AF}$, for the
complete range of hole concentration. We show that the key parameters of the
phase diagram, the $T_c$ dome, and the pseudogap temperature $T^*$, emerge from
the statistical properties of the pairon disordered state. In this approach,
the superconducting and the pseudogap states appear as inseparable phenomena.
The condensation energy, which fixes the critical temperature, is directly
proportional to the {\it correlation energy} between pairons and {\it not} to
the energy gap, contrary to conventional superconductors.
  When the correlation energy between pairons is suppressed by fluctuations,
either thermally, by disorder, or in the vortex core, the pseudogap state of
disordered pairons is obtained. We attribute the unique features of cuprate
superconductivity to this order-disorder transition in real space, which
clearly differs from the BCS mechanism. Our predictions are in quantitative
agreement with low-temperature tunneling and photoemission spectroscopy
experiments.
