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CATEGORIES:Probability
SUMMARY:Fluctuations in the number of level set components
of planar Gaussian fields - Stephen Muirhead (Que
en Mary)
DTSTART;TZID=Europe/London:20200121T140000
DTEND;TZID=Europe/London:20200121T150000
UID:TALK138085AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138085
DESCRIPTION:Gaussian fields are a model of spatial noise\, and
in many applications it is useful to understand t
he geometric structure of their level sets. There
is a natural classification of geometric functiona
ls of the level sets as either `local' (e.g. lengt
h of the level sets\, volume of the excursion sets
\, Euler characteristic of the excursion sets) or
'non-local' (e.g. number of components of the leve
l/excursion sets\, percolation of the level/excurs
ion sets) depending on whether there exists an int
egral representation for the functional. In the ca
se of `local' functionals\, first order properties
(e.g. asymptotics for the mean) are easily derive
d from the Kac-Rice formula\, and second order pro
perties (e.g. asymptotics for the variance\, centr
al limit theorems) can also be established via Wei
ner chaos expansions (Kratz--Leon '11\, Estrade--L
eon '16\, Marinucci--Rossi--Wigman '17\, Nourdin--
Peccati--Rossi '17 etc). For the `non-local' numbe
r of level/excursion sets the analysis is more cha
llenging\, and while first order properties were e
stablished 10 years ago by Nazarov--Sodin using er
godic theoretical techniques\, up until now there
have been essentially no second order results. In
this talk I will discuss some first steps in this
directions\, namely proving lower bounds on the va
riance which are of `correct' order. Joint work wi
th Dmitry Belyaev and Michael McAuley (University
of Oxford).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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