Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling features of two special Markov chains involving total disasters   Catastrophe Markov chain population models have received a lot of attention
in the recent past. We herewith consider two special cases of such models
involving total disasters, both in discrete and in continuous-time. Depending
on the parameters range, the two models can show up a recurrence/transience
transition and, in the critical case, a positive/null recurrence transition.
The collapse transition probabilities are chosen in such a way that the models
are exactly solvable and, in case of positive recurrence, intimately related to
the extended Sibuya and Pareto-Zipf distributions whose divisibility and
self-decomposability properties are shown relevant. The study includes:
existence and shape of the invariant measure, time-reversal, return time to the
origin, contact probability at the origin, extinction probability, height and
length of the excursions, a renewal approach to the fraction of time spent in
the catastrophic state, scale function, first time to collapse and
first-passage times, divisibility properties.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ