Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct and inverse results for popular differences in trees of positive
  dimension   We establish analogues for trees of results relating the density of a set $E
\subset \mathbb{N}$, the density of its set of popular differences, and the
structure of $E$. To obtain our results, we formalise a correspondence
principle of Furstenberg and Weiss which relates combinatorial data on a tree
to the dynamics of a Markov process. Our main tools are Kneser-type inverse
theorems for sets of return times in measure-preserving systems. In the ergodic
setting we use a recent result of the first author with Bj\"orklund and
Shkredov and a stability-type extension (proved jointly with Shkredov); we also
prove a new result for non-ergodic systems.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph