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SUMMARY:Height gaps of planar Brownian motion and Brownian loop soup - Ant
 oine Jego (EPFL - Ecole Polytechnique Fédérale de Lausanne)
DTSTART:20240711T130000Z
DTEND:20240711T133000Z
UID:TALK215599@talks.cam.ac.uk
DESCRIPTION:This talk will be focused on two recent results with Titus Lup
 u and Wei Qian where we derive height gap properties of certain fields acr
 oss CLE/SLE loops. The first result below can be heuristically thought of 
 as a limiting case of the second result.\nFirstly\, we show that the occup
 ation measure of planar Brownian motion exhibits a constant height gap of 
 5/&pi\; across its outer boundary. Secondly\, we construct a field natural
 ly coupled with a subcritical Brownian loop soup and show that it exhibits
  a constant height gap across CLE&kappa\; loops. This latter result is a g
 eneralisation of the celebrated results of Schramm--Sheffield and Miller--
 Sheffield concerning the height gap of the Gaussian free field across SLE4
 /CLE4&nbsp\;curves.
LOCATION:Seminar Room 1\, Newton Institute
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