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DTSTAMP:20260405T175607Z
UID:1616513400@ist.ac.at
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DESCRIPTION:Speaker: Perla Sousi\nhosted by M. Beiglböck\, N. Berestycki\,
  L. Erdös\, J. Maas\, F. Toninelli\nAbstract: A uniform spanning tree 
 of Z^4 can be thought of as the ‘’uniform measure’’ on trees  of
  Z^4. The past of 0 in the uniform spanning tree is the finite componen
 t that is disconnected from infinity when 0 is deleted from the tree. We 
 establish the logarithmic corrections to the probabilities that the past c
 ontains a path of length n\, that it has volume at least n and that it rea
 ches the boundary of the box of side length n around 0. Dimension 4 is the
  upper critical dimension for this model in the sense that in higher dimen
 sions it exhibits "mean-field" critical behaviour. An important part of ou
 r proof is the study of the Newtonian capacity of a loop erased random wal
 k in 4 dimensions. This is joint work with Tom Hutchcroft.
LOCATION:Online via Zoom\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Perla Sousi: The uniform spanning tree in 4 dimensions
URL:https://talks-calendar.ista.ac.at/events/3109
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