Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitivity of mixing times, an example   We construct a family of growing finite bounded degree rooted graphs, $G_n$,
in which the mixing time for simple random walk, starting at the root, is order
$\log |G_n|$. Yet after a quasi - isometry, the ratio of $|G_n|$ over the
mixing time grows arbitrarily slow to infinity.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg