Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant transports of stationary random measures and mass-stationarity   We introduce and study invariant (weighted) transport-kernels balancing
stationary random measures on a locally compact Abelian group. The first main
result is an associated fundamental invariance property of Palm measures,
derived from a generalization of Neveu's exchange formula. The second main
result is a simple sufficient and necessary criterion for the existence of
balancing invariant transport-kernels. We then introduce (in a nonstationary
setting) the concept of mass-stationarity with respect to a random measure,
formalizing the intuitive idea that the origin is a typical location in the
mass. The third main result of the paper is that a measure is a Palm measure if
and only if it is mass-stationary.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio