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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
Speaker:Perla Sousi
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  • In category "Seminar"
  • In group "(Maths) Probability and statistics"
  • By 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.

Speaker

Perla Sousi

  • http://www.statslab.cam.ac.uk/~ps422/

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https://zoom.us/j/94645772345

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Sebastian Andres

sebastian.andres@manchester.ac.uk

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