Geodesic
On an almost all version of the Balog-Szemeredi-Gowers theorem
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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We deduce, as a consequence of the arithmetic removal lemma, an almost-all version of the Balog-Szemerédi-Gowers theorem: For any $K\geq 1$ and $\varepsilon > 0$, there exists $δ= δ(K,\varepsilon)>0$ such that the following statement holds: if $|A+_ΓA| \leq K|A|$ for some $Γ\geq (1-δ)|A|^2$, then there is a subset $A' \subset A$ with $|A'| \geq (1-\varepsilon)|A|$ such that $|A'+A'| \leq |A+_ΓA| + \varepsilon |A|$. We also discuss issues around quantitative bounds in this statement, in particular showing that when $A \subset \mathbb{Z}$ the dependence of $δ$ on $ε$ cannot be polynomial for any fixed $K>2$.
Publié le : 
@article{DAS_2019_a8,
     author = {Xuancheng Shao},
     title = {On an almost all version of the {Balog-Szemeredi-Gowers} theorem},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a8/}
}
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AU  - Xuancheng Shao
TI  - On an almost all version of the Balog-Szemeredi-Gowers theorem
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a8/
LA  - en
ID  - DAS_2019_a8
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%0 Journal Article
%A Xuancheng Shao
%T On an almost all version of the Balog-Szemeredi-Gowers theorem
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a8/
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Xuancheng Shao. On an almost all version of the Balog-Szemeredi-Gowers theorem. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a8/