Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A vector-valued almost sure invariance principle for random expanding on
  average cocycles   We obtain a quenched vector-valued almost sure invariance principle (ASIP)
for random expanding on average cocycles. This is achieved by combining the
adapted version of Gou\"{e}zel's approach for establishing ASIP and the recent
construction of the so-called adapted norms, which in some sense eliminate the
non-uniformity of the decay of correlations. For real-valued observables, we
also show that the martingale approximation technique is applicable in our
setup, and that it yields the ASIP with better error rates. Finally, we present
an example showing the necessity of a scaling condition, answering a question
of the first and third authors.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom