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Product set phenomena for countable groups

Martin Björklund (Institutionen för material- och tillverkningsteknik, Avancerad oförstörande provning) ; A. Fish
Advances in Mathematics (0001-8708). Vol. 275 (2015), p. 47-113.
[Artikel, refereegranskad vetenskaplig]

We develop in this paper novel techniques to analyze local combinatorial structures in product sets of two subsets of a countable group which are "large" with respect to certain classes of (not necessarily invariant) means on the group. Our methods heavily utilize the theory of C*-algebras and random walks on groups. As applications of our methods, we extend and quantify a series of recent results by Jin, Bergelson-Furstenberg-Weiss, Beiglbock-Bergelson-Fish, Griesmer and Di Nasso-Lupini to general countable groups.

Nyckelord: Ergodic Ramsey theory, Random walks on groups, Topological dynamics, Additive combinatorics, Mathematics



Denna post skapades 2015-05-11.
CPL Pubid: 216952

 

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Institutioner (Chalmers)

Institutionen för material- och tillverkningsteknik, Avancerad oförstörande provning

Ämnesområden

Matematik

Chalmers infrastruktur