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CATEGORIES:Probability
SUMMARY:Connectivity properties of random interlacements -
Balazs Rath (ETH\, Zurich)
DTSTART;TZID=Europe/London:20120131T163000
DTEND;TZID=Europe/London:20120131T173000
UID:TALK35925AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/35925
DESCRIPTION:We consider the interlacement Poisson point proces
s on the space of doubly-infinite Zd-valued traje
ctories\, d >=3. This random spatial process was r
ecently introduced by Sznitman in order to describ
e the local picture left by the trace of a random
walk when it visits a positive fraction of a large
d-dimensional torus.\n\nThe present talk summariz
es recent joint work with Artem Sapozhnikov (ETH).
We show that almost surely every two points of th
e random interlacement are connected via at most
ceiling(d/2) trajectories\, and that this number i
s optimal. With a variant of this connectivity arg
ument we also prove that the graph induced by the
random interlacements is almost surely transient
and that Bernoulli percolation on this graph has a
non-trivial phase transition in wide enough slabs
.\n\nThese results strongly suggest that despite t
he 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 0W
B
CONTACT:
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