Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multidimensional record patterns   Multidimensional record patterns are random sets of lattice points defined by
means of a recursive stochastic construction. The patterns thus generated owe
their richness to the fact that the construction is not based on a total order,
except in one dimension, where usual records in sequences of independent random
variables are recovered. We derive many exact results on the statistics of
multidimensional record patterns on finite samples drawn on hypercubic lattices
in any dimension $D$. The most detailed analysis concerns the two-dimensional
situation, where we also investigate the distribution of the landing position
of the record point which is closest to the origin. Asymptotic expressions for
the full distribution and the moments of the number of records on large
hypercubic samples are also obtained. The latter distribution is related to
that of the largest of $D$ standard Gaussian variables.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio