  We study the existence, uniqueness and rate of decay of correlation of
equilibrium measures associated to robust classes of non-uniformly expanding
local diffeomorphisms and H\"older continuous potentials. The approach used in
this paper is the spectral analysis of the Ruelle-Perron-Frobenius transfer
operator. More precisely, we combine the expanding features of the
eigenmeasures of the transfer operator with a Lasota-Yorke type inequality to
prove the existence of an unique equilibrium measure with fast decay of
correlations.
