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SUMMARY:Relative Entropy and Fisher Information - Marius Junge (University
  of Illinois\; University of Illinois at Urbana-Champaign)
DTSTART:20180727T113000Z
DTEND:20180727T121500Z
UID:TALK108430@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We show that in finite dimension the set of generates satisfyi
 ng a stable version of the log-sobolev inequality for the Fisher informati
 on is dense. The results is based on&nbsp\; a new algebraic property \, va
 lid for subordinates semigroups&nbsp\; for sublabplacians&nbsp\; on compac
 t Riemann manifolds which is then transferred to matrix algebras. Even in 
 the commutative setting the inequalities for subordinated sublaplacians ar
 e entirely new. We also found counterexample for why a naive approach via 
 hypercontractivity is not expected to work in a matrix-valued setting\, si
 milar&nbsp\; to results by Bardet and collaborators.  <br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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