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TZID:Europe/Budapest
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UID:6c98i6lk8k978vuclcb2v819lk@google.com
CATEGORIES:{lang hu}Sztochasztika szeminárium{/lang}{lang en}Stochastics seminar{/lang}
SUMMARY:Fodor Ferenc (SZTE): Random approximations of convex bodies by balls
LOCATION:Szeged, Aradi vértanúk tere 1., Riesz terem.
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:\nAbstract: Approximation of convex bodies by random polytopes is one of th
e oldest topics of geometric probability. Its origins go back to the famous
four-point problem of Sylvester in the 1860s. The most frequently investig
ated model of random polytopes is when one takes the convex hull of n i.i.d
. uniform random points in a d-dimensional convex body K. Certain geometric
quantities of the random polytopes, such as volume, surface area, etc, app
roach those of K with high probability as n tends to infinity. It is one of
the important questions how fast this convergence is and how it depends on
the facial structure of K.\n\nIn this talk we will consider a variant of t
he uniform model in which we generate the random objects (called random bal
l-polytopes) by the intersection of equal radius closed balls instead of cl
osed half-spaces. We will primarily investigate the asymptotic behaviour of
the number of facets of random ball-polytopes in smooth convex bodies as n
tends to infinity. We will generalize some earlier joint results with P. K
evei and V. Vigh from the plane to arbitrary dimensions. We will prove the
interesting phenomenon that the expected number of proper facets of uniform
random ball-polytopes in a ball tends to a constant that depends only on t
he dimension.
DTSTAMP:20230209T053138Z
DTSTART;TZID=Europe/Budapest:20180321T140000
DTEND;TZID=Europe/Budapest:20180321T160000
SEQUENCE:0
TRANSP:OPAQUE
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