Perla Sousi - The uniform spanning tree in 4 dimensions
|Dates:||10 February 2021|
|Times:||15:00 - 16:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Perla Sousi (Cambridge) will speak in the Probability seminar.
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.
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