Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of potential winners in Bradley-Terry model in random
  environment   We consider a Bradley-Terry model in random environment where each player
faces each other once. More precisely the strengths of the players are assumed
to be random and we study the influence of their distributions on the
asymptotic number of potential winners.First we prove that under mild
assumptions, mainly on their moments, if the strengths are unbounded, the
asymptotic probability that the best player wins is 1. We also exhibit a
sufficient convexity condition to obtain the same result when the strengths are
bounded. When this last condition fails, the number of potential winners grows
at a rate depending on the tail of the distribution of strengths. We also study
the minimal strength required for an additional player to win in this last
case.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol