  Three topics concerning infrared effective lattice QCD are discussed.
(1)Perfect lattice action of infrared SU(3) QCD and perfect operators for the
static potential are analytically given when we assume two-point monopole
interactions alone. The assumption seems to be justified from numerical
analyses of pure SU(3) QCD in maximally abelian gauge. (2)Gauge invariance of
monopole dominance can be proved theoretically if the gauge invariance of
abelian dominance is proved. The gauge invariance of monopole condensation
leads us to confinement of abelian neutral but color octet states after abelian
projection. (3)A stochastic gauge fixing method is developed to study the gauge
dependence of the Abelian projection, which interpolates between the maximally
abelian (MA) gauge and no gauge fixing. Abelian dominance for the heavy quark
potential holds even in the gauge which is far from Maximally Abelian one.
