  An interesting case of string/black hole transition occurs in two-dimensional
non-critical string theory dressed with a compact CFT. In these models the high
energy densities of states of perturbative strings and black holes have the
same leading behavior when the Hawking temperature of the black hole is equal
to the Hagedorn temperature of perturbative strings. We compare the first
subleading terms in the black hole and closed string entropies in this setting
and argue that the entropy interpolates between these expressions as the energy
is varied. We compute the subleading correction to the black hole entropy for a
specific simple model.
