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SUMMARY:Matrix Concentration and Free Probability - Afonso Bandeira (ETH Z
 ürich)
DTSTART:20240312T140000Z
DTEND:20240312T150000Z
UID:TALK212341@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Concentration inequalities such as Matrix Bernstein inequality
  have played an important role in many areas of pure and applied mathemati
 cs. These inequalities are intimately related to the celebrated noncommuta
 tive Khintchine inequality of Lust-Piquard and Pisier. In the middle of th
 e 2010's\, Tropp improved the dimensional dependence of this inequality in
  certain settings by leveraging cancellations due to non-commutativity of 
 the underlying random matrices\, giving rise to the question of whether su
 ch dependency could be removed.\nIn this talk we leverage ideas from Free 
 Probability to fully remove the dimensional dependence in a range of insta
 nces\, yielding optimal bounds in many settings of interest. As a byproduc
 t we develop matrix concentration inequalities that capture non-commutativ
 ity (or\, to be more precise\, ``freeness'')\, improving over Matrix Berns
 tein in a range of instances. No background knowledge of Free Probability 
 will be assumed in the talk.\nJoint work with March Boedihardjo and Ramon 
 van Handel.
LOCATION:MR12
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