Regularity lemma for distal structures

@article{Chernikov2015RegularityLF,
  title={Regularity lemma for distal structures},
  author={Artem Chernikov and Sergei Starchenko},
  journal={Journal of the European Mathematical Society},
  year={2015}
}
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… 
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