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SUMMARY:Concentration and Free Probability - Afonso Bandeira (ETH Zürich)
DTSTART:20240312T140000Z
DTEND:20240312T150000Z
UID:TALK209572@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Matrix Concentration inequalities such as Matrix Bernstein ine
 quality have played an important role in many areas of pure and applied ma
 thematics. These inequalities are intimately related to the celebrated non
 commutative Khintchine inequality of Lust-Piquard and Pisier. In the middl
 e of the 2010's\, Tropp improved the dimensional dependence of this inequa
 lity in certain settings by leveraging cancellations due to non-commutativ
 ity of the underlying random matrices\, giving rise to the question of whe
 ther such dependency could be removed.\nIn this talk we leverage ideas fro
 m Free Probability to fully remove the dimensional dependence in a range o
 f instances\, yielding optimal bounds in many settings of interest. As a b
 yproduct we develop matrix concentration inequalities that capture non-com
 mutativity (or\, to be more precise\, ``freeness'')\, improving over Matri
 x Bernstein in a range of instances. No background knowledge of Free Proba
 bility will be assumed in the talk.\nJoint work with March Boedihardjo and
  Ramon van Handel.
LOCATION:MR12\, Centre for Mathematical Sciences
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