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SUMMARY:Connectivity properties of random interlacements - Balazs Rath (ET
 H\, Zurich)
DTSTART:20120131T163000Z
DTEND:20120131T173000Z
UID:TALK35925@talks.cam.ac.uk
CONTACT:24872
DESCRIPTION:We consider the interlacement Poisson point process on the spa
 ce of  doubly-infinite Zd-valued trajectories\, d >=3. This random spatial
  process was recently introduced by Sznitman in order to describe the loca
 l picture left by the trace of a random walk when it visits a positive fra
 ction of a large d-dimensional torus.\n\nThe present talk summarizes recen
 t joint work with Artem Sapozhnikov (ETH). We show that almost surely ever
 y two points of the random  interlacement are connected via at most ceilin
 g(d/2) trajectories\, and that this number is optimal. With a variant of t
 his connectivity argument we  also prove that the graph induced by the ran
 dom interlacements is almost surely transient and that Bernoulli percolati
 on on this graph has a non-trivial phase transition in wide enough slabs.\
 n\nThese results strongly suggest that despite the long-range dependencies
  present in the model\, the geometry of the random interlacement graph is 
 similar to that of the underlying lattice Zd\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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