Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On weighted depths in random binary search trees   Following the model introduced by Aguech, Lasmar and Mahmoud [Probab. Engrg.
Inform. Sci. 21 (2007) 133-141], the weighted depth of a node in a labelled
rooted tree is the sum of all labels on the path connecting the node to the
root. We analyze weighted depths of nodes with given labels, the last inserted
node, nodes ordered as visited by the depth first search process, the weighted
path length and the weighted Wiener index in a random binary search tree. We
establish three regimes of nodes depending on whether the second order
behaviour of their weighted depths follows from fluctuations of the keys on the
path, the depth of the nodes, or both. Finally, we investigate a random
distribution function on the unit interval arising as scaling limit for
weighted depths of nodes with at most one child.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con