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SUMMARY:Update Tolerance in Uniform Spanning Forests - Tom Hutchcroft (UBC
 )
DTSTART:20160308T150000Z
DTEND:20160308T160000Z
UID:TALK64961@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION: The uniform spanning forests (USFs) of an infinite graph G ar
 e defined to be infinite volume limits of uniformly chosen spanning trees 
 of finite subgraphs of G. These limits can be taken with respect to two ex
 tremal boundary conditions\, yielding the free uniform spanning forest (FU
 SF) and wired uniform spanning forest (WUSF). While the wired uniform span
 ning forest has been quite well understood since the seminal paper of Benj
 amini\, Lyons\, Peres and Schramm (’01)\, the FUSF is less understood\, 
 and some very basic questions about it remain open. In this talk I will in
 troduce a new tool in the study of USFs\, called update tolerance\, and de
 scribe how update tolerance can be used to prove\, among other things\, th
 at the FUSF has either one or infinitely many connected components on any 
 infinite Cayley graph\, and that components of either the FUSF and WUSF ar
 e indistinguishable from each other by invariantly defined properties on a
 ny infinite Cayley graph. Another crucial component of these proofs is the
  Mass-Transport Principle\, which I will also give an introduction to.\n\n
 Based in part on joint work with Asaf Nachmias.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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