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SUMMARY:Disorder\, entropy and harmonic functions - Hugo Duminil (Geneva)
DTSTART:20120214T141500Z
DTEND:20120214T151500Z
UID:TALK36028@talks.cam.ac.uk
CONTACT:24872
DESCRIPTION:Since the work of Yau in 1975\, where a Liouville property for
  positive harmonic\nfunctions on complete manifolds with non-negative Ricc
 i curvature is proved\, the\nstructure of various spaces of harmonic funct
 ions have been at the heart of\ngeometric analysis. We extend this questio
 n to the random context\, with an\nemphasize on the infinite cluster of pe
 rcolation. We will prove that for almost\nevery supercritical-cluster of p
 ercolation\, there are no non-constant sublinear\nharmonic functions. The 
 main ingredient of the proof is a quantitative\, annealed\nversion of the 
 Kaimanovich-Vershik entropy argument. We will also mention several\nopen p
 roblems and conjectures on the behavior of harmonic functions on stationar
 y\nrandom graphs.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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