Zero-one laws for events with positional symmetries
Fuente:
arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916661245771776 |
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| author | Ayach, Yahya Khairallah, Anthony Manoukian, Tia Mchaimech, Jad Salha, Adam Taati, Siamak |
| author_facet | Ayach, Yahya Khairallah, Anthony Manoukian, Tia Mchaimech, Jad Salha, Adam Taati, Siamak |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-one laws for events with positional symmetries Ayach, Yahya Khairallah, Anthony Manoukian, Tia Mchaimech, Jad Salha, Adam Taati, Siamak Probability Information Theory 60F20, 60G09, 94A15 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. |
| title | Zero-one laws for events with positional symmetries |
| topic | Probability Information Theory 60F20, 60G09, 94A15 |
| url | https://arxiv.org/abs/2406.14902 |