Factoring Probabilities on Compact Groups.
STANFORD UNIV CA DEPT OF STATISTICS
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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
- Statistics and Probability