Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The limiting distribution of the hook length of a randomly chosen cell
  in a random Young diagram   Let $p(n)$ be the number of all integer partitions of the positive integer
$n$ and let $\lambda$ be a partition, selected uniformly at random from among
all such $p(n)$ partitions. It is known that each partition $\lambda$ has a
unique graphical representation, composed by $n$ non-overlapping cells in the
plane called Young diagram. As a second step of our sampling experiment, we
select a cell $c$ uniformly at random from among all $n$ cells of the Young
diagram of the partition $\lambda$. For large $n$, we study the asymptotic
behavior of the hook length $Z_n=Z_n(\lambda,c)$ of the cell $c$ of a random
partituion $\lambda$. This two-step sampling procedure suggests a product
probability measure, which assigns the probability $1/np(n)$ to each pair
$(\lambda,c)$. With respect to this probability measure, we show that the
random variable $\pi Z_n/\sqrt{6n}$ converges weakly, as $n\to\infty$, to a
random variable whose probability density function equals $6y/\pi^2 (e^y-1)$ if
$0<y<\infty$, and zero elsewhere.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess