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SUMMARY:Asymptotic normality of certain transformation averages - Peter Or
 banz — University College London
DTSTART:20191018T130000Z
DTEND:20191018T140000Z
UID:TALK130042@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Consider a large random structure--a stochastic process on the
  line\, a random graph\, a random field on the grid--and a function that d
 epends only on a small part of the structure. Now use elements of a transf
 ormation group to 'move' the domain of the function over the structure\, a
 nd average over the collected values. It is known from ergodic theory that
  such averages converge to (conditional) expectations\, if (i) the transfo
 rmations leave the distribution invariant and (ii) the group is sufficient
 ly nice. I will present results that show they are also asymptotically nor
 mal\, under a suitable mixing condition. Several known central limit theor
 ems for stationary random fields\, graphon models\, etc emerge as special 
 cases.
LOCATION:MR12
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