Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Results on Joint Record Events   Let $X_1,X_2,\dots$ be independent and identically distributed random
variables on the real line with a joint continuous distribution function $F$.
The stochastic behavior of the sequence of subsequent records is well known.
Alternatively to that, we investigate the stochastic behavior of arbitrary
$X_j,X_k,j<k$, under the condition that they are records, without knowing their
orders in the sequence of records. The results are completely different. In
particular it turns out that the distribution of $X_k$, being a record, is not
affected by the additional knowledge that $X_j$ is a record as well. On the
contrary, the distribution of $X_j$, being a record, is affected by the
additional knowledge that $X_k$ is a record as well. If $F$ has a density, then
the gain of this additional information, measured by the corresponding
Kullback-Leibler distance, is $j/k$, independent of $F$. We derive the limiting
joint distribution of two records, which is not a bivariate extreme value
distribution. We extend this result to the case of three records. In a special
case we also derive the limiting joint distribution of increments among
records.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga