Local limits of spatial inhomogeneous random graphs

Abstract Consider a set of n vertices, where each vertex has location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube , and weight associated to it. Construct random graph by placing edges independently for pair with probability function distance between locations weights. Under appropriate integrability assumptions on edge probabilities imply sparseness model, after appropriately blowing up locations, we prove local limit this sequence (countably) infinite given homogeneous Poisson point process, having weights which are independent identically distributed copies limiting Our set-up covers many sparse geometric models literature, including inhomogeneous graphs (GIRGs), hyperbolic graphs, continuum scale-free percolation, weight-dependent connection models. We degree distribution mixed typical integrable, obtain convergence results various measures clustering our as consequence convergence. Finally, byproduct argument, doubly logarithmic lower bound distances general setting.