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CATEGORIES:Probability
SUMMARY:Limit theory for statistics of random geometric st
ructures - Joe Yukich (Lehigh University)
DTSTART;TZID=Europe/London:20171107T161500
DTEND;TZID=Europe/London:20171107T171500
UID:TALK86461AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/86461
DESCRIPTION:Questions arising in stochastic geometry and appli
ed geometric probability often involve the quantif
ying the behavior of statistics of large random ge
ometric structures. Such structures arise in diver
se settings and include:\n\n(i) Point processes of
dependent points in R^d\, including determinantal
\, permanental\, and Gibbsian point sets\, as well
as the zeros of Gaussian analytic functions\,\n\n
(ii) Simplicial complexes in topological data anal
ysis\,\n\n(iii) Graphs on random vertex sets in Eu
clidean space\,\n\n(iv) Random polytopes generated
by random data.\n\nGlobal features of geometric s
tructures are often expressible as a sum of local
contributions. In general the local contributions
have short range spatial interactions but complica
ted long range dependence. In this survey talk we
review stabilization methods for establishing the
limit theory for statistics of geometric structure
s. Stabilization provides conditions under which t
he behavior of a sum of local contributions is sim
ilar to that of a sum of independent identically d
istributed random variables.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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