تقرير
Lumpings of Algebraic Markov Chains arise from Subquotients
| العنوان: | Lumpings of Algebraic Markov Chains arise from Subquotients |
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| المؤلفون: | Pang, C. Y. Amy |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Probability |
| الوصف: | A function on the state space of a Markov chain is a "lumping" if observing only the function values gives a Markov chain. We give very general conditions for lumpings of a large class of algebraically-defined Markov chains, which include random walks on groups and other common constructions. We specialise these criteria to the case of descent operator chains from combinatorial Hopf algebras, and, as an example, construct a "top-to-random-with-standardisation" chain on permutations that lumps to a popular restriction-then-induction chain on partitions, using the fact that the algebra of symmetric functions is a subquotient of the Malvenuto-Reutenauer algebra. Comment: 36 pages. Minor update from v2 after peer-review, with numerical sectioning as in the published version. (v2 was majorly reworked from v1, with new results in sections 3.5/II.D and 3.6/II.E, and new examples in Part I/Section 2.) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10959-018-0834-0 |
| URL الوصول: | http://arxiv.org/abs/1508.01570 |
| رقم الأكسشن: | edsarx.1508.01570 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10959-018-0834-0 |
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