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CATEGORIES:Statistics
SUMMARY:Concentration and Free Probability - Afonso Bandei
ra (ETH Zürich)
DTSTART;TZID=Europe/London:20240312T140000
DTEND;TZID=Europe/London:20240312T150000
UID:TALK209572AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209572
DESCRIPTION:Matrix Concentration inequalities such as Matrix B
ernstein inequality have played an important role
in many areas of pure and applied mathematics. The
se inequalities are intimately related to the cele
brated noncommutative Khintchine inequality of Lus
t-Piquard and Pisier. In the middle of the 2010's\
, Tropp improved the dimensional dependence of thi
s inequality in certain settings by leveraging can
cellations due to non-commutativity of the underly
ing random matrices\, giving rise to the question
of whether such dependency could be removed.\nIn t
his talk we leverage ideas from Free Probability t
o fully remove the dimensional dependence in a ran
ge of instances\, yielding optimal bounds in many
settings of interest. As a byproduct we develop ma
trix concentration inequalities that capture non-c
ommutativity (or\, to be more precise\, ``freeness
'')\, improving over Matrix Bernstein in a range o
f instances. No background knowledge of Free Proba
bility will be assumed in the talk.\nJoint work wi
th March Boedihardjo and Ramon van Handel.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Dr Sergio Bacallado
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