Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic cellular automata with general alphabets letting a Markov
  chain invariant   This paper is devoted to probabilistic cellular automata (PCA) on
$\mathbb{N}$, $\mathbb{Z}$ or $\mathbb{Z}/n\mathbb{Z}$, depending of two
neighbors, with a general alphabet $E$ (finite or infinite, discrete or not).
We study the following question: under which conditions does a PCA possess a
Markov chain as invariant distribution? Previous results in the literature give
some conditions on the transition matrix (for positive rate PCA) when the
alphabet $E$ is finite. Here we obtain conditions on the transition kernel of
PCA with a general alphabet $E$. In particular, we show that the existence of
an invariant Markov chain is equivalent to the existence of a solution to a
cubic integral equation.
  One of the difficulties to pass from a finite alphabet to a general alphabet
comes from some problems of measurability, and a large part of this work is
devoted to clarify these issues.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin