Skip to content

SAS

Seminar

Ergodic theory and strong randomness notions

Franklin, J (University of Connecticut)
Thursday 05 July 2012, 14:30-15:00

Seminar Room 1, Newton Institute

Abstract

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.

Presentation

[pdf ]

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧