Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity lemma for distal structures   It is known that families of graphs with a semialgebraic edge relation of
bounded complexity satisfy much stronger regularity properties than arbitrary
graphs, and that they can be decomposed into very homogeneous semialgebraic
pieces up to a small error (e.g., see [33, 2, 16, 18]). We show that similar
results can be obtained for families of graphs with the edge relation uniformly
definable in a structure satisfying a certain model theoretic property called
distality, with respect to a large class of generically stable measures.
Moreover, distality characterizes these strong regularity properties. This
applies in particular to graphs definable in arbitrary $o$-minimal structures
and in $p$-adics.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ