Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local limits of spatial inhomogeneous random graphs   Consider a set of $n$ vertices, where each vertex has a location in
$\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$,
and a weight associated to it. Construct a random graph by placing edges
independently for each vertex pair with a probability that is a function of the
distance between the locations, and the vertex weights.
  Under appropriate integrability assumptions on the edge probabilities that
imply sparseness of the model, after appropriately blowing up the locations, we
prove that the local limit of this random graph sequence is the (countably)
infinite random graph on $\mathbb{R}^d$ with vertex locations given by a
homogeneous Poisson point process, having weights which are i.i.d. copies of
limiting vertex weights. Our setup covers many sparse geometric random graph
models from the literature, including Geometric Inhomogeneous Random Graphs
(GIRGs), Hyperbolic Random Graphs, Continuum Scale-Free Percolation and
Weight-dependent Random Connection Models.
  We prove that the limiting degree distribution is mixed Poisson, and the
typical degree sequence is uniformly integrable, and obtain convergence results
on various measures of clustering in our graphs as a consequence of local
convergence. Finally, as a by-product of our argument, we prove a doubly
logarithmic lower bound on typical distances in this general setting.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph