Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The diameter of uniform spanning trees in high dimensions   We show that the diameter of a uniformly drawn spanning tree of a connected
graph on $n$ vertices which satisfies certain high-dimensionality conditions
typically grows like $\Theta(\sqrt{n})$. In particular this result applies to
expanders, finite tori $\mathbb{Z}_m^d$ of dimension $d \geq 5$, the hypercube
$\{0,1\}^m$, and small perturbations thereof.

19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc