  CaCu$_{3}$Ti$_{4}$O$_{12}$ (CCTO) has a large dielectric permittivity that is
independent of the probing frequency near the room temperature, which
complicated due to the existence of several dynamic processes. Here, we
consider the combined effects of localized charge carriers (polarons) and
thermally activated charge carriers using a recently proposed statistical model
to fit and understand the permittivity of CCTO measured at different
frequencies over the whole temperature range accessible by our experiments. We
found that the small permittivity at the lowest temperature is related to
polaron frozen, while at higher temperatures the rapid increase is associated
with the thermal excitation of polarons inducing the Maxwell-Wagner effect, and
the final increase of the permittivity is attributed to the thermally activated
conductivity. Such analysis enables us to separate the contributions from
localized polarons and conductive charge carriers and quantify their activation
energies.
