Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic tree algorithms   In this paper, a general tree algorithm processing a random flow of arrivals
is analyzed. Capetanakis--Tsybakov--Mikhailov's protocol in the context of
communication networks with random access is an example of such an algorithm.
In computer science, this corresponds to a trie structure with a dynamic input.
Mathematically, it is related to a stopped branching process with exogeneous
arrivals (immigration). Under quite general assumptions on the distribution of
the number of arrivals and on the branching procedure, it is shown that there
exists a positive constant $\lambda_c$ so that if the arrival rate is smaller
than $\lambda_c$, then the algorithm is stable under the flow of requests, that
is, that the total size of an associated tree is integrable. At the same time,
a gap in the earlier proofs of stability in the literature is fixed. When the
arrivals are Poisson, an explicit characterization of $\lambda_c$ is given.
Under the stability condition, the asymptotic behavior of the average size of a
tree starting with a large number of individuals is analyzed. The results are
obtained with the help of a probabilistic rewriting of the functional equations
describing the dynamics of the system. The proofs use extensively this
stochastic background throughout the paper. In this analysis, two basic limit
theorems play a key role: the renewal theorem and the convergence to
equilibrium of an auto-regressive process with a moving average.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an