Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative ergodic theorems for actions of groups of polynomial growth   We strengthen the maximal ergodic theorem for actions of groups of polynomial
growth to a form involving jump quantity, which is the sharpest result among
the family of variational or maximal ergodic theorems. As a consequence, we
deduce in this setting the quantitative ergodic theorem, in particular, the
upcrossing inequalities with exponential decay. The ideas or techniques involve
probability theory, non-doubling Calder\'on-Zygmund theory, almost
orthogonality argument and some delicate geometric argument involving the balls
and the cubes on the group equipped with a not necessarily doubling measure.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas