Statistical Properties of Martin-L\"of Random Sequences
Matthew Pancia
TL;DR
This paper investigates the statistical characteristics of Martin-Löf random sequences, demonstrating they satisfy classical probabilistic laws and are normal, unlike weakly random sequences.
Contribution
It establishes that Martin-Löf randomness implies adherence to key statistical laws and normality, providing a rigorous foundation for understanding their properties.
Findings
Martin-Löf random sequences obey Strong Law of Large Numbers
They satisfy the Law of the Iterated Logarithm
They are normal sequences
Abstract
We study the statistical properties of random numbers under the Martin-L\"of definition of randomness, proving that random numbers obey analogues of Strong Law of Large Numbers, the Law of the Iterated Logarithm, and that they are normal. We also show that weakly (1-)random numbers do not share these properties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Methods and Mixture Models