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SUMMARY:On the number of level sets of smooth Gaussian fields - Dmitry Bel
 yaev (Oxford)
DTSTART:20221129T140000Z
DTEND:20221129T150000Z
UID:TALK183203@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The number of zeroes or\, more generally\, level crossings of 
 a\nGaussian process is a classical subject that goes back to the works of\
 nKac and Rice who studied zeroes of random polynomials.  The number of\nze
 roes or level crossings has two natural generalizations in higher\ndimensi
 ons. One can either look at the size of the level set or the\nnumber of co
 nnected components. The surface area of a level set could be computed in a
  similar way using Kac-Rice formulas. On the other hand\,\nthe number of t
 he connected components is a `non-local' quantity which\nis notoriously ha
 rd to work with. The law of large numbers has been\nestablished by Nazarov
  and Sodin about ten years ago. In this talk\, we\nwill briefly discuss th
 eir work and then discuss the recent progress in\nestimating the variance 
 and deriving the central limit theorem. The talk\nis based on joint work w
 ith M. McAuley and S. Muirhead.
LOCATION:MR12\, Centre for Mathematical Sciences
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