Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Random invariant densities for Markov operator cocycles and random mean
  ergodic theorem
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th