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CATEGORIES:Probability
SUMMARY:Matrix Concentration and Free Probability - Afonso
Bandeira (ETH Zürich)
DTSTART;TZID=Europe/London:20240312T140000
DTEND;TZID=Europe/London:20240312T150000
UID:TALK212341AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/212341
DESCRIPTION:Concentration inequalities such as Matrix Bernstei
n inequality have played an important role in many
areas of pure and applied mathematics. These ineq
ualities are intimately related to the celebrated
noncommutative Khintchine inequality of Lust-Piqua
rd and Pisier. In the middle of the 2010's\, Tropp
improved the dimensional dependence of this inequ
ality in certain settings by leveraging cancellati
ons due to non-commutativity of the underlying ran
dom matrices\, giving rise to the question of whet
her such dependency could be removed.\nIn this tal
k we leverage ideas from Free Probability to fully
remove the dimensional dependence in a range of i
nstances\, yielding optimal bounds in many setting
s of interest. As a byproduct we develop matrix co
ncentration inequalities that capture non-commutat
ivity (or\, to be more precise\, ``freeness'')\, i
mproving over Matrix Bernstein in a range of insta
nces. No background knowledge of Free Probability
will be assumed in the talk.\nJoint work with Marc
h Boedihardjo and Ramon van Handel.
LOCATION:MR12
CONTACT:HoD Secretary\, DPMMS
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