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arXiv · 1105.0663

Uncomputably noisy ergodic limits

Jeremy Avigad
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Abstract

V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n f. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given epsilon.

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Jeremy Avigad. 2011-05-03. Uncomputably noisy ergodic limits. https://doi.org/10.1215/00294527-1716757

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