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STACS
2009
Springer

Randomness on Computable Probability Spaces - A Dynamical Point of View

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Randomness on Computable Probability Spaces - A Dynamical Point of View
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the statistical behavior of the system (Birkhoff’s pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every mixing computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications. Contents
Péter Gács, Mathieu Hoyrup, Cristoba
Added 20 May 2010
Updated 20 May 2010
Type Conference
Year 2009
Where STACS
Authors Péter Gács, Mathieu Hoyrup, Cristobal Rojas
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