Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral dimension and random walks on the two dimensional uniform
  spanning tree   We study simple random walk on the uniform spanning tree on Z^2 . We obtain
estimates for the transition probabilities of the random walk, the distance of
the walk from its starting point after n steps, and exit times of both
Euclidean balls and balls in the intrinsic graph metric. In particular, we
prove that the spectral dimension of the uniform spanning tree on Z^2 is 16/13
almost surely.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th