Alpern, Steven and Prasad, V. S. (2005) Rotational (and other) representations of stochastic matrices. CDAM research report series (CDAM-LSE-2005-13). Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.
Full text not available from this repository.Abstract
Joel E. Cohen (1981) conjectured that any stochastic matrix P = fpi;jg could be represented by some circle rotation f in the following sense: For some par- tition fSig of the circle into sets consisting of nite unions of arcs, we have (*) pi;j = (f (Si) \ Sj) = (Si), where denotes arc length. In this paper we show how cycle decomposition techniques originally used (Alpern, 1983) to establish Cohen�s conjecture can be extended to give a short simple proof of the Coding Theorem, that any mixing (that is, PN > 0 for some N) stochastic matrix P can be represented (in the sense of * but with Si merely measurable) by any aperiodic measure preserving bijection (automorphism) of a Lesbesgue proba- bility space. Representations by pointwise and setwise periodic automorphisms are also established. While this paper is largely expository, all the proofs, and some of the results, are new.
| Item Type: | Monograph (Report) |
|---|---|
| Official URL: | http://www.cdam.lse.ac.uk |
| Additional Information: | © 2005 the authors |
| Divisions: | Mathematics Management |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 23 Oct 2008 10:17 |
| Last Modified: | 12 Dec 2024 05:42 |
| URI: | http://eprints.lse.ac.uk/id/eprint/13931 |
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