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SUMMARY:Wei Qian (City University of Hong Kong)
DTSTART:20230308T140000Z
DTEND:20230308T150000Z
DTSTAMP:20260423T035532Z
UID:ADPS/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ADPS/17/">Co
 nformally invariant fields out of Brownian loop soups</a>\nby Wei Qian (Ci
 ty University of Hong Kong) as part of Abu Dhabi Stochastics Seminar\n\n\n
 Abstract\nFor each central charge c in (0\,1]\, we construct a conformally
  invariant field which is a measurable function of the local time field L 
 of the Brownian loop soup with intensity c and i.i.d. signs given to each 
 cluster. This field is canonically associated to L\, in a sense which is s
 imilar to the isomorphism theory that associates the Gaussian free field t
 o the loop soup with critical intensity. Isomorphisms between Brownian mot
 ions and random fields were previously developed by Symanzik\, Brydges-Fr
 öhlich-Spencer\, Dynkin and Le Jan in several different settings.\nIn a k
 ey intermediate step\, we obtain the crossing exponent for the event that 
 a cluster in the subcritical loop soup passes near a given point. Among ot
 her things\, it allows us to deduce that the Minkowski gauge function of a
  cluster in a loop soup with intensity c in (0\,1)\, which is t^2 f(t) for
  some f(t)=|\\log t|^{1-c/2+o(1)}.\nIn the end\, I will present several co
 njectures about this family of fields. This talk is based on joint works i
 n progress with Antoine Jego (EPFL) and Titus Lupu (CNRS).\n
LOCATION:https://researchseminars.org/talk/ADPS/17/
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