A real density of disorder-induced resonators with a high
quality factor, Q >> 1, in a film with fluctuating
refraction index is calculated theoretically. We demonstrate
that for a given kl > 1, where k is the light wave vector, and
l is the transport mean free path, when on average the light
propagation is diffusive, the likelihood for finding a random
resonator increases dramatically with increasing the size of
the scatterers, or, more precisely, the correlation radius of
the disorder. Parameters of most probable resonators as
functions of Q and kl are found.
*Work performed under the auspices of NSF under grant No. DMR-0202790 and Petroleum Research Fund under grant No. PRF 37890-AC6.