Matrix Concentration and Free Probability

Add to your list(s) Download to your calendar using vCal

• Afonso Bandeira (ETH Zürich)
• Tuesday 12 March 2024, 14:00-15:00
• MR12.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

Concentration inequalities such as Matrix Bernstein inequality have played an important role in many areas of pure and applied mathematics. These inequalities are intimately related to the celebrated noncommutative Khintchine inequality of Lust-Piquard and Pisier. In the middle of the 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 such dependency could be removed. In this talk we leverage ideas from Free Probability to fully remove the dimensional dependence in a range of instances, yielding optimal bounds in many settings of interest. As a byproduct we develop matrix concentration inequalities that capture non-commutativity (or, to be more precise, ``freeness’‘), improving over Matrix Bernstein in a range of instances. No background knowledge of Free Probability will be assumed in the talk. Joint work with March Boedihardjo and Ramon van Handel.

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator
• bld31

Note that ex-directory lists are not shown.