Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bound on the expected size of intrinsic ball   We give a short proof of Theorem 1.2 (i) from the paper "The Alexander-Orbach
conjecture holds in high dimensions" by G. Kozma and A. Nachmias. We show that
the expected size of the intrinsic ball of radius r is at most Cr if the
susceptibility exponent is at most 1. In particular, this result follows if the
so-called triangle condition holds.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga