Algorithmic Randomness For Amenable Groups
Logic
2018-03-23 v3
Abstract
We develop the theory of algorithmic randomness for the space where is a finite alphabet and is a computable amenable group. We give an effective version of the Shannon-McMillan-Breiman theorem in this setting. We also extend a result of Simpson equating topological entropy and Hausdorff dimension. This proof makes use of work of Ornstein and Weiss which we also present.
Keywords
Cite
@article{arxiv.1802.03831,
title = {Algorithmic Randomness For Amenable Groups},
author = {Adam R. Day},
journal= {arXiv preprint arXiv:1802.03831},
year = {2018}
}
Comments
The proof of theorem 7 is incorrect - it only shows the desired result on a computable subsequence