Random walks on quasisymmetric functions

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Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several well-studied random walks are now realized this way: Stanley's QS-distribution results from endomorphisms given by evaluation maps, a-shuffles result from the a-th convolution power of the universal character, and the Tchebyshev operator of the second kind introduced recently by Ehrenborg and Readdy yields traditional riffle shuffles. A conjecture of Ehrenborg regarding the spectra for a family of random walks on ab-words is proven. A theorem of Stembridge from the theory of enriched P-partitions is also recovered as a special case.
25 pages

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Combinatorics, Probability, 05E99; 16W30; 60C05; 60J10

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http://salesiana.dossiersoluciones.com/handle/123456789/137706

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.1477
 http://arxiv.org/abs/0709.1477

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arXiv