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DTSTART:19700329T010000
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CATEGORIES:Probability
SUMMARY:On the number of level sets of smooth Gaussian fie
lds - Dmitry Belyaev (Oxford)
DTSTART;TZID=Europe/London:20221129T140000
DTEND;TZID=Europe/London:20221129T150000
UID:TALK183203AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183203
DESCRIPTION:The number of zeroes or\, more generally\, level c
rossings of a\nGaussian process is a classical sub
ject that goes back to the works of\nKac and Rice
who studied zeroes of random polynomials. The num
ber of\nzeroes or level crossings has two natural
generalizations in higher\ndimensions. One can eit
her look at the size of the level set or the\nnumb
er of connected components. The surface area of a
level set could be computed in a similar way using
Kac-Rice formulas. On the other hand\,\nthe numbe
r of the connected components is a `non-local' qua
ntity which\nis notoriously hard to work with. The
law of large numbers has been\nestablished by Naz
arov and Sodin about ten years ago. In this talk\,
we\nwill briefly discuss their work and then disc
uss the recent progress in\nestimating the varianc
e and deriving the central limit theorem. The talk
\nis based on joint work with M. McAuley and S. Mu
irhead.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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