Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice deformations in the Heisenberg group   The space of deformations of the integer Heisenberg group under the action of
$\textrm{Aut}(H(\mathbb{R}))$ is a homogeneous space for a non-reductive group.
We analyze its structure as a measurable dynamical system and obtain mean and
variance estimates for Heisenberg lattice point counting in measurable subsets
of $\mathbb{R}^3$; in particular, we obtain a random Minkowski-type theorem.
Unlike the Euclidean case, we show there are necessary geometric conditions on
the sets that satisfy effective variance bounds.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th