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 $betain(0,1)$ . 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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机译：我们在无限字母上构建混合过程，在有限字母上遍历遍历过程，对于它们，相邻长度为$ n $的块之间的香农互信息增长为$ n ^ {beta} $，其中$ betain（0,1）$。这些过程是对非遍历的Santa Fe过程的修改，这些过程是在自然语言建模的上下文中引入的。后一过程的相互信息率相似，并且也在本文中确定。作为辅助结果，表明混合过程的无限直接产物也在混合。
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