Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911372892176384 |
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| author | Austin, Tim Bowen, Lewis Shriver, Christopher |
| author_facet | Austin, Tim Bowen, Lewis Shriver, Christopher |
| contents | We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17387 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property Austin, Tim Bowen, Lewis Shriver, Christopher Dynamical Systems Probability 37A35 We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ 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. |
| title | Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property |
| topic | Dynamical Systems Probability 37A35 |
| url | https://arxiv.org/abs/2312.17387 |