Miklós Pálfia

These slides contain new results about stochastic approximation with operator means. First I report on new results related to generalized Karcher means and law of large numbers for such. This is a continuation of earlier work on the subject in Thompson metric spaces. Then new results on Wasserstein means of positive operators are reviewed, in particular their definition, construction and approximation are considered. This parallels the theory of the Karcher mean developed in Thompson metric spaces, but the underlying geometry is totally different, in particular we don’t know too much about the constructed Banach-Finsler structure that is instrumental to have exponential contracting properties of associated flows and thus law of large numbers type of results.

The slides are about a combination of two topics, the first part on an extended strong law of large numbers, while from slide 37 onwards they are about noncommutative concave and monotone functions. https://erdoscenter.renyi.hu/events/focused-workshop-quantum-renyi-divergences

I gave this talk recently on the Preserver webinar, here is the recorded video of the talk: https://drive.google.com/file/d/1tESm8m4R-Dn-1k7zFPS1WKiyEbQEnMmp/view?usp=sharing

Slides are available for my talk here: https://palfiamiklos.com/wp-content/uploads/2020/10/palfia-pw2020.pdf

I presented these slides a few times, for instance at ILAS2019 and a conference at LSU honoring Jimmie D. Lawson’s 70th working anniversary there. They are available here: https://palfiamiklos.com/wp-content/uploads/2020/10/sturmsllnkarcher.pdf

My slides from the Taussky-Todd lecture at ILAS2017 are available here.

The slides of the talk that I gave on Loewner’s theorem in several variables in 2016 at the annual operator algebras workshop in RIMS, and then at OTOA2016 are available here. The talk is a presentation of the results of the paper https://arxiv.org/abs/1405.5076.

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