Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An ergodic correspondence principle, invariant means and applications   A theorem due to Hindman states that if $E$ is a subset of $\mathbb{N}$ with
$d^*(E)>0$, where $d^*$ denotes the upper Banach density, then for any
$\varepsilon>0$ there exists $N \in \mathbb{N}$ such that
$d^*\left(\bigcup_{i=1}^N(E-i)\right) > 1-\varepsilon$. Curiously, this result
does not hold if one replaces the upper Banach density $d^*$ with the upper
density $\bar{d}$. Originally proved combinatorially, Hindman's theorem allows
for a quick and easy proof using an ergodic version of Furstenberg's
correspondence principle. In this paper, we establish a variant of the ergodic
Furstenberg's correspondence principle for general amenable (semi)-groups and
obtain some new applications, which include a refinement and a generalization
of Hindman's theorem and a characterization of countable amenable minimally
almost periodic groups.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph