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

Autor:	Austin, Tim, Bowen, Lewis, Shriver, Christopher
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Probability 37A35
Druh dokumentu:	Working Paper
Popis:	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. Comment: Version 2: improvements to Section 4
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.17387 Zobrazit plný text záznamu View this record from Arxiv