The thesis proves the quenched invariance principle for two models of long-range random conductances on the rectangular lattice of dimension at least 2. The conductances are assumed to be either i.i.d. or ergodic and to decay as a power of the distance, analogous to jumping measures of stable processes. Under certain moment conditions on the distribution, we prove the quenched invariance principle as well as large scale parabolic Harnack inequality.
