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SUMMARY:Asymptotic number of connected components of nodal sets of random 
 functions - Matthis Lehmkuehler\, ETH Zurich
DTSTART:20191023T150000Z
DTEND:20191023T160000Z
UID:TALK133774@talks.cam.ac.uk
CONTACT:Jan Bohr
DESCRIPTION:*Abstract.* Consider a random smooth (Gaussian) field and asso
 ciate to it its (zero level) nodal set i.e. all points that map to zero. M
 any questions can be asked about these nodal sets: total surface measure\,
  number of connected components\, percolative properties\, etc. The focus 
 of the talk will be to address the second question and explain Nazarov and
  Sodin's proof (2016) of a corresponding law of large numbers. I will also
  (briefly) link the random theory to the deterministic problem of understa
 nding the nodal sets associated to the eigenfunctions of the Laplace opera
 tor.
LOCATION:MR14\, Centre for Mathematical Sciences
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