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Geometric and Functional Analysis

, Volume 23, Issue 1, pp 1–41 | Cite as

Expansion in SL 2 \({(\mathbb{R})}\) and monotone expanders

  • Jean Bourgain
  • Amir YehudayoffEmail author
Article

Abstract

This work presents an explicit construction of a family of monotone expanders, which are bi-partite expander graphs whose edge-set is defined by (partial) monotone functions. The family is (roughly) defined by the Möbius action of SL 2 \({\mathbb{R}}\) on the interval [0,1]. A key part of the proof is a product-growth theorem for certain subsets of SL 2 \({\mathbb{R}}\) . This extends recent results on finite/compact groups to the non-compact scenario. No other proof-of-existence for monotone expanders is known.

Keywords

Cayley Graph Explicit Construction Universal Constant Product Theorem Matrix Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsTechnion–IITHaifaIsrael

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