University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Ergodic theory and strong randomness notions

Ergodic theory and strong randomness notions

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

If you have a question about this talk, please contact Mustapha Amrani.

Semantics and Syntax: A Legacy of Alan Turing

There has been a great deal of interest recently in the connection between algorithmic randomness and ergodic theory, which naturally leads to the question of how much one can say if the transformations in question need not be ergodic. We have essentially reversed a result of V’yugin and shown that if an element of the Cantor space is not Martin-Löf random, then there is a computable function and a computable transformation for which this element is not typical with respect to the ergodic theorem. More recently, we have shown that every weakly 2-random element of the Cantor space is typical with respect to the ergodic theorem for every lower semicomputable function and computable transformation. I will explain the proof of the latter result and discuss the technical difficulties present in producing a full characterization.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity