We study the quenched invariance principle for random conductance models with long range jumps on Zd, where transition probability from x to y is, average, comparable |x−y|−(d+α) α∈(0,2) but is allowed be degenerate. Under some moment conditions conductance, we prove that scaling limit of Markov process a symmetric α-stable Lévy Rd. The well-known corrector method in homogenization theory does ...