Factoring Probabilities on Compact Groups.
Abstract
When can a probability P be factored as P1 * P2? This problem arises in efficient generation of pseudo random integers and permutations. It is thus natural to think of P defined on a group. We show that any strictly positive measure can be factored. The uniform distribution can be factored in a non-trivial way for any compact group having more than three elements. If it is required that U = P* P, then factorization is possible if and only if the group is not Abelian or the product of the quarternions and a finite number of two element groups. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 02, 1981
- Accession Number
- ADA109663
Entities
People
- Mehrdad Shashahani
- Persi Diaconis
Organizations
- Stanford University