Quenched invariance principle for <inline-formula><tex-math id="M1">$ L^2 $</tex-math></inline-formula>-integrable long range random walk in balanced environments

In this paper, we study the quenched invariance principle for $ L^2 $-integrable long-range random walk in balanced random environments. As a key ingredient for the proof, we will also prove a kind of ABP type maximal inequality for a general non-local operator in $ \mathbb Z^d $.