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SUMMARY:Lower variance bounds for Poisson functionals
DTSTART;VALUE=DATE-TIME:20220804T140000Z
DTEND;VALUE=DATE-TIME:20220804T142000Z
DTSTAMP;VALUE=DATE-TIME:20240914T202537Z
UID:indico-contribution-200-1209@conference2.aau.at
DESCRIPTION:Lower bounds for variances are often needed to derive central
limit theorems. In this talk\, we establish a specific lower bound for the
variance of a Poisson functional that uses the difference operator of Mal
liavin calculus. \nPoisson functionals\, i.e. random variables that depend
on a Poisson process\, are widely used in stochastic geometry. In this ta
lk\, we show how to apply our lower variance bound to statistics of spatia
l random graphs\, the $L^p$ surface area of random polytopes and the volum
e of excursion sets of Poisson shot noise processes. This talk is based on
joint work with M. Schulte.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1209/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1209/
END:VEVENT
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SUMMARY:A simplified second-order Gaussian Poincaré inequality with appli
cation to random subgraph counting
DTSTART;VALUE=DATE-TIME:20220804T133000Z
DTEND;VALUE=DATE-TIME:20220804T135000Z
DTSTAMP;VALUE=DATE-TIME:20240914T202537Z
UID:indico-contribution-200-1208@conference2.aau.at
DESCRIPTION:A simplified second-order Gaussian Poincaré inequality for no
rmal approximation of functionals over infinitely many Rademacher random v
ariables is derived. It is based on a new bound for the Kolmogorov distanc
e between a general Rademacher functional and a Gaussian random variable\,
which is established by means of the discrete Malliavin-Stein method and
is of independent interest. As an application\, standardized subgraph coun
ts in the Erdős-Rényi random graph are discussed.\n\nhttps://conference2
.aau.at/event/131/contributions/1208/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1208/
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