Mar 23, 2021

The uniform spanning tree in 4 dimensions

VIENNA PROBABILITY SEMINAR

Date: March 23, 2021 | 4:30 pm – 5:15 pm
Speaker: Perla Sousi, University of Cambridge
Location: Online via Zoom

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 component that is disconnected from infinity when 0 is deleted from the tree. We establish the logarithmic corrections to the probabilities that the past contains a path of length n, that it has volume at least n and that it reaches 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 dimensions it exhibits "mean-field" critical behaviour. An important part of our proof is the study of the Newtonian capacity of a loop erased random walk in 4 dimensions. This is 
joint work with Tom Hutchcroft.

More Information:

Date:
March 23, 2021
4:30 pm – 5:15 pm

Speaker:
Perla Sousi, University of Cambridge

Location:
Online via Zoom

Contact:

Birgit Oosthuizen-Noczil

Email:
birgit.oosthuizen-noczil@ist.ac.at

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