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A sharp threshold for van der Waerden's theorem in random subsets
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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We establish sharpness for the threshold of van der Waerden's theorem in random subsets of $\mathbb{Z}/n\mathbb{Z}$. More precisely, for $k\geq 3$ and $Z\subseteq \mathbb{Z}/n\mathbb{Z}$ we say $Z$ has the van der Waerden property if any two-colouring of $Z$ yields a monochromatic arithmetic progression of length $k$. Rödl and Ruciński (1995) determined the threshold for this property for any k and we show that this threshold is sharp. The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on the recently developed container method for independent sets in hypergraphs by Balogh, Morris and Samotij (2015) and by Saxton and Thomason (2015).
Publié le : 
@article{DAS_2016_a12,
     author = {E. Friedgut and H. H\`an and Y. Person and M. Schacht},
     title = {A sharp threshold for van der {Waerden's} theorem in random subsets},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a12/}
}
TY  - JOUR
AU  - E. Friedgut
AU  - H. Hàn
AU  - Y. Person
AU  - M. Schacht
TI  - A sharp threshold for van der Waerden's theorem in random subsets
JO  - Discrete analysis
PY  - 2016
UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a12/
LA  - en
ID  - DAS_2016_a12
ER  - 
%0 Journal Article
%A E. Friedgut
%A H. Hàn
%A Y. Person
%A M. Schacht
%T A sharp threshold for van der Waerden's theorem in random subsets
%J Discrete analysis
%D 2016
%U http://geodesic.mathdoc.fr/item/DAS_2016_a12/
%G en
%F DAS_2016_a12
E. Friedgut; H. Hàn; Y. Person; M. Schacht. A sharp threshold for van der Waerden's theorem in random subsets. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a12/