Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quenched law of large numbers and quenched central limit theorem for
  multi-player leagues with ergodic strengths   We propose and study a new model for competitions, specifically sports
multi-player leagues where the initial strengths of the teams are independent
i.i.d. random variables that evolve during different days of the league
according to independent ergodic processes. The result of each match is random:
the probability that a team wins against another team is determined by a
function of the strengths of the two teams in the day the match is played.
  Our model generalizes some previous models studied in the physical and
mathematical literature and is defined in terms of different parameters that
can be statistically calibrated. We prove a quenched -- conditioning on the
initial strengths of the teams -- law of large numbers and a quenched central
limit theorem for the number of victories of a team according to its initial
strength.
  To obtain our results, we prove a theorem of independent interest. For a
stationary process $\xi=(\xi_i)_{i\in \mathbb{N}}$ satisfying a mixing
condition and an independent sequence of i.i.d. random variables $(s_i)_{i\in
\mathbb{N}}$, we prove a quenched -- conditioning on $(s_i)_{i\in\mathbb{N}}$
-- central limit theorem for sums of the form
$\sum_{i=1}^{n}g\left(\xi_i,s_i\right)$, where $g$ is a bounded measurable
function. We highlight that the random variables $g\left(\xi_i,s_i\right)$ are
not stationary conditioning on $(s_i)_{i\in\mathbb{N}}$.

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th