Pré-Publication, Document De Travail Année : 2025

Symbol Frequencies in Surjective Cellular Automata

Résumé

We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the sequence of measures have full support as well? The initial measure of our solution is not a product measure, and in this case the question remains open. To this end, we present a tool for studying the frequencies of symbols in preimages of surjective cellular automata, and prove some basic results about it. However, we show that by itself it is not enough to solve the stricter question in the positive.

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hal-05026614 , version 1 (09-04-2025)

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  • HAL Id : hal-05026614 , version 1

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Benjamin Hellouin de Menibus, Ville Salo, Ilkka Törmä. Symbol Frequencies in Surjective Cellular Automata. 2025. ⟨hal-05026614⟩
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