Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the scaling limit of finite vertex transitive graphs with large
  diameter   Let $(X_n)$ be an unbounded sequence of finite, connected, vertex transitive
graphs such that $ |X_n | = o(diam(X_n)^q)$ for some $q>0$. We show that up to
taking a subsequence, and after rescaling by the diameter, the sequence $(X_n)$
converges in the Gromov Hausdorff distance to a torus of dimension $<q$,
equipped with some invariant Finsler metric. The proof relies on a recent
quantitative version of Gromov's theorem on groups with polynomial growth
obtained by Breuillard, Green and Tao. If $X_n$ is only roughly transitive and
$|X_n| = o\bigl({diam(X_n)^{\delta}}\bigr)$ for $\delta > 1$ sufficiently
small, we prove, this time by elementary means, that $(X_n)$ converges to a
circle.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas