Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-type linear fractional branching processes in varying environments
  with asymptotically constant mean matrices   Consider two-type linear-fractional branching processes in varying
environments with asymptotically constant mean matrices. Let $\nu$ be the
extinction time. Under certain conditions, we show that both $P(\nu=n)$ and
$P(\nu>n)$ are asymptotically the same as some functions of the products of
spectral radii of the mean matrices. We also give an example for which
$P(\nu=n)$ decays with various speeds such as $\frac{c}{n(\log n)^2},$
$\frac{c}{n^\beta},\beta >1$ et al. which are very different from the ones of
homogeneous multitype Galton-Watson processes.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph