Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluctuation bounds for continuous time branching processes and
  nonparametric change point detection in growing networks   Motivated by applications, both for modeling real world systems as well as in
the study of probabilistic systems such as recursive trees, the last few years
have seen an explosion in models for dynamically evolving networks. The aim of
this paper is two fold: (a) develop mathematical techniques based on continuous
time branching processes (CTBP) to derive quantitative error bounds for
functionals of a major class of these models about their large network limits;
(b) develop general theory to understand the role of abrupt changes in the
evolution dynamics of these models using which one can develop non-parametric
change point detection estimators. In the context of the second aim, for fixed
final network size $n$ and a change point $\tau(n) < n$, we consider models of
growing networks which evolve via new vertices attaching to the pre-existing
network according to one attachment function $f$ till the system grows to size
$\tau(n)$ when new vertices switch their behavior to a different function $g$
till the system reaches size $n$. With general non-explosivity assumptions on
the attachment functions $f,g$, we consider both the standard model where
$\tau(n) = \Theta(n)$ as well as the \emph{quick big bang model} when $\tau(n)
= n^\gamma$ for some $0<\gamma <1$. Proofs rely on a careful analysis of an
associated \emph{inhomogeneous} continuous time branching process. Techniques
developed in the paper are robust enough to understand the behavior of these
models for any sequence of change points $\tau(n)\to\infty$. This paper derives
rates of convergence for functionals such as the degree distribution; the same
proof techniques should enable one to analyze more complicated functionals such
as the associated fringe distributions.

3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn