Symbol Frequencies in Surjective Cellular Automata
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909572675928064 |
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| author | de Menibus, Benjamin Hellouin Törmä, Ilkka Salo, Ville |
| author_facet | de Menibus, Benjamin Hellouin Törmä, Ilkka Salo, Ville |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symbol Frequencies in Surjective Cellular Automata de Menibus, Benjamin Hellouin Törmä, Ilkka Salo, Ville Dynamical Systems 37B15, 37A60 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. |
| title | Symbol Frequencies in Surjective Cellular Automata |
| topic | Dynamical Systems 37B15, 37A60 |
| url | https://arxiv.org/abs/2504.06058 |