Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unified framework for limit results in Chemical Reaction Networks on
  multiple time-scales   If $(X^N)_{N=1,2,...}$ is a sequence of Markov processes which solve the
martingale problems for some operators $(G^N)_{N=1,2,...}$, it is a classical
task to derive a limit result as $N\to\infty$, in particular a weak process
limit with limiting operator $G$. For slow-fast systems $X^N = (V^N, Z^N)$
where $V^N$ is slow and $Z^N$ is fast, $G^N$ consists of two (or more) terms,
and we are interested in weak convergence of $V^N$ to some Markov process $V$.
In this case, for some $f\in \mathcal D(G)$, the domain of $G$, depending only
on $v$, the limit $Gf$ can sometimes be derived by using some $g_N\to 0$
(depending on $v$ and $z$), and study convergence of $G^N (f + g_N) \to Gf$. We
develop this method further in order to obtain functional Laws of Large Numbers
(LLNs) and Central Limit Theorems (CLTs). We then apply our general result to
various examples from Chemical Reaction Network theory. We show that we can
rederive most limits previously obtained, but also provide new results in the
case when the fast-subsystem is first order. In particular, we allow that fast
species to be consumed faster than they are produced, and we derive a CLT for
Hill dynamics with coefficient~2.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex