Product set phenomena for countable groups
Journal article, 2015

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.

Mathematics

Additive combinatorics

Topological dynamics

Ergodic Ramsey theory

Random walks on groups

Author

Martin Björklund

Chalmers, Materials and Manufacturing Technology, Advanced Non-destructive Testing

A. Fish

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 275 47-113

Subject Categories

Mathematics

DOI

10.1016/j.aim.2015.02.005

More information

Created

10/7/2017