Zero-one laws for events with positional symmetries
| Autor: | Ayach, Yahya, Khairallah, Anthony, Manoukian, Tia, Mchaimech, Jad, Salha, Adam, Taati, Siamak |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We use an information-theoretic argument due to O'Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identically distributed random variables is deterministic (i.e., has a probability of either 0 or 1). The i.i.d. condition can be relaxed. This result encompasses the Hewitt-Savage zero-one law and the ergodicity of the Bernoulli process, but also applies to other scenarios such as infinite random graphs and simple renormalization processes. Comment: 15 pages, 4 figures |
| Databáze: | arXiv |
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