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SUMMARY:Tensor freeness and central limit theorem - Sang-Jun Park (CNRS (C
 entre national de la recherche scientifique))
DTSTART:20241202T143000Z
DTEND:20241202T145000Z
UID:TALK224632@talks.cam.ac.uk
DESCRIPTION:Voiculescu's notion of asymptotic free independence applies to
  a wide range of random matrices\, including those that are independent an
 d unitary invariant. In this work\, we generalize this notion by consideri
 ng random matrices with a tensor product structure that are invariant unde
 r the action of local-unitaries. We show that\, given the existence of lim
 it 'tensor moments' described by tuples of permutations\, an independent f
 amily of local-unitary invariant random matrices satisfies a new kind of i
 ndependence in the limit\, which we will call 'tensor freen independence'.
  This can be defined via vanishing mixed 'tensor free cumulants'\, allowin
 g the joint moments of tensor free elements to be described in terms of th
 at of individual elements. Additionally\, we propose a tensor free version
  of the central limit theorem\, which extends and recovers the recent resu
 lts on central limit theorem for tensor products of free variables. This i
 s joint work with Ion Nechita.
LOCATION:Seminar Room 1\, Newton Institute
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