Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On extinction time distribution of a 2-type linear-fractional branching
  process in a varying environment with asymptotically constant mean matrices   In this paper we study a 2-type linear-fractional branching process in
varying environment with asymptotically constant mean matrices. Let $\nu$ be
the extinction time and for $k\ge1$ let $M_k$ be the mean matrix of offspring
distribution of individuals of the $(k-1)$-th generation. Under certain
conditions, we show that $P(\nu=n)$ and $P(\nu>n)$ are asymptotically
equivalent to some functions of products of spectral radii of the mean
matrices. This paper complements a former result [arXiv: 2007.07840] which
requires in addition a condition $\forall k\ge1,\rm{det}(M_k)<-\varepsilon$ for
some $\varepsilon>0.$ Such a condition excludes a large class of mean matrices.
As byproducts, we also get some results on asymptotics of products of
nonhomogeneous matrices which have their own interests.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int