Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the reduction of a random basis   For $g < n$, let $b\_1,...,b\_{n-g}$ be $n - g$ independent vectors in
$\mathbb{R}^n$ with a common distribution invariant by rotation. Considering
these vectors as a basis for the Euclidean lattice they generate, the aim of
this paper is to provide asymptotic results when $n\to +\infty$ concerning the
property that such a random basis is reduced in the sense of {\sc Lenstra,
Lenstra & Lov\'asz}. The proof passes by the study of the process
$(r\_{g+1}^{(n)},r\_{g+2}^{(n)},...,r\_{n-1}^{(n)})$ where $r\_j^{(n)}$ is the
ratio of lengths of two consecutive vectors $b^*\_{n-j+1}$ and $b^*\_{n-j}$
built from $(b\_1,...,b\_{n-g})$ by the Gram--Schmidt orthogonalization
procedure, which we believe to be interesting in its own. We show that, as
$n\to+\infty$, the process $(r\_j^{(n)}-1)\_j$ tends in distribution in some
sense to an explicit process $({\mathcal R}\_j -1)\_j$; some properties of this
latter are provided.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph