7 research outputs found
Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems
A pseudorandom point in an ergodic dynamical system over a computable metric
space is a point which is computable but its dynamics has the same statistical
behavior as a typical point of the system.
It was proved in [Avigad et al. 2010, Local stability of ergodic averages]
that in a system whose dynamics is computable the ergodic averages of
computable observables converge effectively. We give an alternative, simpler
proof of this result.
This implies that if also the invariant measure is computable then the
pseudorandom points are a set which is dense (hence nonempty) on the support of
the invariant measure
Computable Measure Theory and Algorithmic Randomness
International audienceWe provide a survey of recent results in computable measure and probability theory, from both the perspectives of computable analysis and algorithmic randomness, and discuss the relations between them