A Hot Spot Proof of the Generalized Wall Theorem

Abstract If a sequence of numbers behaves like a random sequence, do we expect subsequences to also behave like a random sequence? Wall proved that normality of a base-b expansion is preserved along arithmetic progressions. What makes arithmetic progressions special is that they are deterministic sequences, a type of low-complexity sequence. We give a self-contained proof that selection along deterministic sequences preserves normality and provide several interesting examples of nontrivial deterministic sequences.

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