Quenched Invariance Principle for a class of random conductance models with long-range jumps

We study random walks on $\mathbb Z^d$ (with $d\ge 2$) among stationary ergodic random conductances $\{C_{x,y}\colon x,y\in\mathbb Z^d\}$ that permit jumps of arbitrary length. Our focus is on the Quenched Invariance Principle (QIP) which we establish by a combination of corrector methods, functional inequalities and heat-kernel technology assuming that the $p$-th moment of $\sum_{x\in\mathbb Z^d}C_{0,x}|x|^2$ and $q$-th moment of $1/C_{0,x}$ for $x$ neighboring the origin are finite for some $p,q\ge1$ with $p^{-1}+q^{-1}