  By analyzing the dynamical properties of particle production in relativistic
heavy ion collisions, it is possible to characterize the final stage of the
equilibration process occurring in the collision fireball. In this work, we use
the Hagedorn model coupled with non-extensive statistics to evaluate the
transverse momentum spectra of positive pions for various event centrality
classes in Au+Au collisions at RHIC with center-of-mass energies of 62.4GeV/A
and 200GeV/A. We find that, by assuming an energy distribution that
incorporates particle correlations, it is possible to explain the entire
$\pi^{+}$ $p_{T}$ spectrum as measured by RHIC. We find that spectra from
central collisions, when compared to peripheral collisions, are consistent with
a system that has smaller values of the non-extensivity parameter "q" and
higher values of temperature. Comparison between different beam energies also
shows a variation of the "q" parameter. The result is discussed using the
interpretation that the "q" parameter is a measure of particle correlations
within the system. Under this assumption, our results show that more central
collisions are consistent with a system with less particle correlations.
