Uniform Expansion Bounds for Cayley Graphs of$SL_2 (F_p )

Uniform Expansion Bounds for Cayley Graphs of$SL_2 (F_p )

We prove that Cayley graphs of $SL_2 (F_p )$ are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in $SL_2 (F_p )$ .

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Veröffentlicht in:Annals of mathematics 2008-03, Vol.167 (2), p.625-642
Hauptverfasser: Bourgain, Jean, Gamburd, Alex
Format: Artikel
Sprache:eng
Schlagworte:
Adjacency matrix
Combinatorics
Eigenvalues
Graph theory
Group theory
Proof by contradiction
Random walk
Same sex marriage
Vertices
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Zusammenfassung:We prove that Cayley graphs of $SL_2 (F_p )$ are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in $SL_2 (F_p )$ .
ISSN:0003-486X
DOI:10.4007/annals.2008.167.625