Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

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

Publication Date

2018

Source Publication Title

Journal of Theoretical Probability

Publisher

Springer Verlag

DOI

10.1007/s10959-018-0834-0

Link to Publisher's Edition

https://link.springer.com/article/10.1007/s10959-018-0834-0

ISSN (print)

0894-9840

Included in

Mathematics Commons

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