Transience of symmetric nonlocal Dirichlet forms

We establish transience criteria for symmetric nonlocal Dirichlet forms on $L^2({\mathbb{R}}^d;\mathrm{d}x)$ in terms of the coefficient growth rates at infinity. Applying these criteria, we find a necessary and sufficient condition for recurrence of Dirichlet forms of symmetric stable-like with unbounded/degenerate coefficients. This condition indicates that both of the coefficient growth rates of small and big jump parts affect the sample path properties of the associated symmetric jump processes.