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arXiv · 2312.17387

Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property

Tim Austin·Lewis Bowen·Christopher Shriver
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Abstract

We construct an explicit algebraic example of a subshift of finite type over a group $\Gamma$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a direct Bernoulli factor, because its model spaces shatter into exponentially many clusters of sub-exponential size. The example and its analysis are related to random low-density parity-check (LDPC) codes.

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Tim Austin, Lewis Bowen, Christopher Shriver. 2023-12-28. Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property. https://doi.org/10.1017/s147474802510100x

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