Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Destruction of CPE-normality along deterministic sequences   Let $\mu$ be a shift-invariant measure on $\Lambda^{\mathbb N}$, where
$\Lambda$ is a finite or countable alphabet. We say that an increasing sequence
of natural numbers $S=\{s_1,s_2,\dots\}$ preserves (destroys) $\mu$-normality
if, for any $x=(x_1,x_2,...)\in\Lambda^{\mathbb N}$ generic for $\mu$, the
sequence $x|_S=(x_{s_1},x_{s_2},...)$ is (is not) generic for $\mu$. It is
known from Kamae and Weiss that if $\mu$ is i.i.d. then any deterministic
sequence of positive lower density preserves $\mu$-normality. We show that
deterministic sequencess of positive upper density and lower density less than
one destroy $\mu$-normality for any non-i.i.d. measure $\mu$ with completely
positive entropy (CPE). This generalizes Heersink and Vandehey's result for
arithmetic progressions and the Gauss measure (associated to the continued
fraction transformation). We give several examples showing that, outside the
class of measures with CPE, $\mu$-normality preservation can coexist with
nearly any combination of three parameters: determinism of $S$ (or its lack),
entropy of $\mu$ (zero or positive), and disjointness (or its lack) between
$\mu$ and the measures derived from $S$.

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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: nlin