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SUMMARY:Every planar graph with the Liouville property is amenable - Johan
 nes Carmesin (Cambridge)
DTSTART:20151103T163000Z
DTEND:20151103T173000Z
UID:TALK61089@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We introduce a strengthening of the notion of transience for p
 lanar\nmaps in order to relax the standard condition of bounded degree\nap
 pearing in various results\, in particular\, the existence of\nDirichlet h
 armonic functions proved by Benjamini and Schramm. As a\ncorollary we obta
 in that every planar non-amenable graph admits\nDirichlet harmonic functio
 ns.\nThis is joint work with Agelos Georgakopoulos.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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