Zero-one laws for events with positional symmetries
<|reference_start|>Zero-one laws for events with positional symmetries: 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.<|reference_end|>
@article{ayach2024zero-one,
    title={Zero-one laws for events with positional symmetries},
    author={Yahya Ayach, Anthony Khairallah, Tia Manoukian, Jad Mchaimech, Adam
  Salha, Siamak Taati},
    journal={arXiv preprint arXiv:2406.14902},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14902},
    primaryClass={math.PR cs.IT math.IT}
}