Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: B-urns   The fringe of a B-tree with parameter $m$ is considered as a particular
P\'olya urn with $m$ colors. More precisely, the asymptotic behaviour of this
fringe, when the number of stored keys tends to infinity, is studied through
the composition vector of the fringe nodes. We establish its typical behaviour
together with the fluctuations around it. The well known phase transition in
P\'olya urns has the following effect on B-trees: for $m\leq 59$, the
fluctuations are asymptotically Gaussian, though for $m\geq 60$, the
composition vector is oscillating; after scaling, the fluctuations of such an
urn strongly converge to a random variable $W$. This limit is $\mathbb
C$-valued and it does not seem to follow any classical law. Several properties
of $W$ are shown: existence of exponential moments, characterization of its
distribution as the solution of a smoothing equation, existence of a density
relatively to the Lebesgue measure on $\mathbb C$, support of $W$. Moreover, a
few representations of the composition vector for various values of $m$
illustrate the different kinds of convergence.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn