  We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons
grows exponentially with the mass) emerges automatically in large $N_c$ QCD in
2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space
correlation functions for composite operators constructed from quark and gluon
fields and exploits the fact that the short time behavior of the correlators is
known in QCD. The demonstration relies on one critical assumption: that
perturbation theory accurately describes the trace of the logarithm of a matrix
of point-to-point correlation functions in the regime where the perturbative
corrections to the asymptotically free value are small.
