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SUMMARY:Alberto Chiarini (Eindhoven University of Technology)
DTSTART:20211112T173000Z
DTEND:20211112T183000Z
DTSTAMP:20260423T005657Z
UID:PatC/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/46/">Di
 sconnection and entropic repulsion for the harmonic crystal with random co
 nductances</a>\nby Alberto Chiarini (Eindhoven University of Technology) a
 s part of Probability and the City Seminar\n\n\nAbstract\nWe study level-s
 et percolation of the discrete Gaussian free field on the Euclidean lattic
 e in three and more dimensions\, equipped with uniformly elliptic random c
 onductances. We prove that this percolation model undergoes a non-trivial 
 phase transition at a deterministic level. For a compact set A in \\mathbb
 {R}^d\, we study the disconnection event that the level-set of the field b
 elow a given level disconnects the discrete blow-up of A from the boundary
  of an enclosing box\, in a strongly percolative regime. We present quench
 ed asymptotic upper and lower bounds on this probability in terms of the h
 omogenized capacity of A. The upper and lower bounds concerning disconnect
 ion that we derive are plausibly matching at leading order. In this case\,
  this work shows that conditioning on disconnection leads to an entropic p
 ush-down of the field. (Based on a joint work with M. Nitzschner NYU Coura
 nt)\n
LOCATION:https://researchseminars.org/talk/PatC/46/
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