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SUMMARY:Limit theory for statistics of random geometric structures - Joe Y
 ukich (Lehigh University)
DTSTART:20171107T161500Z
DTEND:20171107T171500Z
UID:TALK86461@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Questions arising in stochastic geometry and applied geometric
  probability often involve the quantifying the behavior of statistics of l
 arge random geometric structures. Such structures arise in diverse setting
 s and include:\n\n(i) Point processes of dependent points in R^d\, includi
 ng determinantal\, permanental\, and Gibbsian point sets\, as well as the 
 zeros of Gaussian analytic functions\,\n\n(ii) Simplicial complexes in top
 ological data analysis\,\n\n(iii) Graphs on random vertex sets in Euclidea
 n space\,\n\n(iv) Random polytopes generated by random data.\n\nGlobal fea
 tures of geometric structures are often expressible as a sum of local cont
 ributions. In general the local contributions have short range spatial int
 eractions but complicated long range dependence. In this survey talk we re
 view stabilization methods for establishing the limit theory for statistic
 s of geometric structures. Stabilization provides conditions under which t
 he behavior of a sum of local contributions is similar to that of a sum of
  independent identically distributed random variables.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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