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arXiv · 2603.17188

Sequential densities of rational languages

Alexi Block Gorman·Dominique Perrin
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Abstract

We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{\mu}$, the sequential density is the ordinary density with respect to $\overline{\mu}$. We also prove that if $(\mu_n)$ is a sequence of invariant probability measures converging in the strong sense to an invariant probability measure $\overline{\mu}$, then the sequential density of every rational language exists for this sequence.

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Alexi Block Gorman, Dominique Perrin. 2026-03-17. Sequential densities of rational languages. https://arxiv.org/abs/2603.17188

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