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SUMMARY:Four-dimensional loop-erased random walk and uniform spanning tree
- Wei Wu (Department of Statistics\, University of Warwick)
DTSTART;VALUE=DATE-TIME:20180514T110000Z
DTEND;VALUE=DATE-TIME:20180514T120000Z
UID:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
DESCRIPTION:Critical lattice models are believed to converge to a free fie
ld in the scaling limit\, at or above their critical dimension. This has b
een established for Ising and \\Phi^4 models for d \\geq 4. We describe a
simple spin model from uniform spanning forests in Z^d whose critical dime
nsion is 4 and prove that the scaling limit is the bi-Laplacian Gaussian f
ield for d\\geq 4. At dimension 4\, there is a logarithmic correction for
the spin-spin correlation and the bi-Laplacian Gaussian field is a log cor
related field. The proof also improves the known mean field picture of LER
W in d=4: we show that the renormalized escape probability (and arm events
) of 4D LERW converge to some "continuum escaping probability". Based on j
oint works with Greg Lawler and Xin Sun. \n\nSpeakers:\nWei Wu (Department
of Statistics\, University of Warwick)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
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DESCRIPTION:Talk:Four-dimensional loop-erased random walk and uniform span
ning tree - Wei Wu (Department of Statistics\, University of Warwick)
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