We present a systematic study of the regularity phenomena for NIP hypergraphs and
connections to the theory of (locally) generically stable measures, providing a model …

Over the past several years, numerous authors have explored model theoretically motivated
combinatorial conditions that ensure that a graph has an efficient regular decomposition in …

We present a systematic study of the regularity phenomena for NIP hypergraphs and
connections to the theory of (locally) generically stable measures, providing a model …

We define a natural notion of higher-order stability and show that subsets of $\mathbb {F}
_p^ n $ that are tame in this sense can be approximately described by a union of low …

We investigate various forms of (model-theoretic) stability for hypergraphs and their
corresponding strengthenings of the hypergraph regularity lemma with respect to partitions …

Szemerédi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently,
several refinements of this seminal result were obtained for special, more structured classes …

The celebrated Erd\H {o} s-Hajnal Conjecture says that in any proper hereditary class of
finite graphs we are guaranteed to have a clique or anti-clique of size $ n^ c $, which is a …

Some years ago, we proved a “stable regularity lemma” showing essentially that Szemerédi’s
celebrated regularity lemma is Page 1 The Bulletin of Symbolic Logic Volume 27, Number 4 …

This is Part 2 in a series of papers about the growth of regular partitions in hereditary
properties $3 $-uniform hypergraphs. The focus of this paper is the notion of weak …

Randomness in the Limit Page 1 Randomness in the Limit Henry Towsner July 13, 2022
DRAFT Page 2 2 Page 3 Contents Preface 7 1 Random and Quasi-random Graphs 9 1.1 …