What's the Entropy of a Random Integer?
5 days ago
- #probability
- #number theory
- #entropy
- The text discusses the entropy of the probability distribution derived from the prime factorization of a random integer.
- It simplifies the problem by considering squarefree integers, linking their prime factor sizes to cycle lengths in random permutations.
- The entropy calculation involves summing contributions from each cycle, leading to an estimated mean entropy of 1.
- Questions are raised about the behavior of entropy and perplexity, suggesting deeper connections to number theory.
- References to Terry Tao's blog posts and a paper by Kontoyiannis are provided for further reading.