Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of combinatorial Markov processes   Every exchangeable Feller process taking values in a suitably nice
combinatorial state space can be constructed by a system of iterated random
Lipschitz functions. In discrete time, the construction proceeds by iterated
application of independent, identically distributed functions, while in
continuous time the random functions occur as the atoms of a time homogeneous
Poisson point process. We further show that every exchangeable Feller process
projects to a Feller process in an appropriate limit space, akin to the
projection of partition-valued processes into the ranked-simplex and
graph-valued processes into the space of graph limits. Together, our main
theorems establish common structural features shared by all exchangeable
combinatorial Feller processes, regardless of the dynamics or resident state
space, thereby generalizing behaviors previously observed for exchangeable
coalescent and fragmentation processes as well as other combinatorial
stochastic processes. If, in addition, an exchangeable Feller process evolves
on a state space satisfying the $n$-disjoint amalgamation property for all
$n\geq1$, then its jump measure can be decomposed explicitly in the sense of
L\'evy--It\^o--Khintchine.

5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph