Ergodic Ramsey theory

Ergodic Ramsey theory

Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory.

Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, when Hillel Furstenberg gave a new proof of this theorem using ergodic theory. It has since produced combinatorial results, some of which have yet to be obtained by other means, and has also given a deeper understanding of the structure of measure-preserving dynamical systems.

ee also

*Arithmetic combinatorics
*Ramsey theory
*Syndetic set
*Piecewise syndetic set
*Thick set
*IP set

References

* [http://arxiv.org/abs/math/0608105 Ergodic Methods in Additive Combinatorics]
* [http://www.math.iupui.edu/~mmisiure/open/VB1.pdf Ergodic Ramsey Theory -an Update]
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