Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks

Details Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks

2011-03-21

arxiv.org/abs/1103.3952v2

Computer Science

Information Theory

21 pages

Scientific paper

We construct mixing processes over an infinite alphabet and ergodic processes over a finite alphabet for which Shannon mutual information between adjacent blocks of length $n$ grows as $n^\beta$, where $\beta\in(0,1)$. The processes are a modification of nonergodic Santa Fe processes, which were introduced in the context of natural language modeling. The rates of mutual information for the latter processes are alike and also established in this paper. As an auxiliary result, it is shown that infinite direct products of mixing processes are also mixing.

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