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.
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Horev fellow—supported by the Taub foundation. This research was supported by Sindey & Ann Grazi Research Fund. Research partially supported by ISF and BSF.
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Bourgain, J., Yehudayoff, A. Expansion in SL 2 \({(\mathbb{R})}\) and monotone expanders. Geom. Funct. Anal. 23, 1–41 (2013). https://doi.org/10.1007/s00039-012-0200-9
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DOI: https://doi.org/10.1007/s00039-012-0200-9