Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Leadership Statistics in Random Structures   The largest component (``the leader'') in evolving random structures often
exhibits universal statistical properties. This phenomenon is demonstrated
analytically for two ubiquitous structures: random trees and random graphs. In
both cases, lead changes are rare as the average number of lead changes
increases quadratically with logarithm of the system size. As a function of
time, the number of lead changes is self-similar. Additionally, the probability
that no lead change ever occurs decays exponentially with the average number of
lead changes.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat