Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov Chains from Descent Operators on Combinatorial Hopf Algebras   We develop a general theory for Markov chains whose transition probabilities
are the coefficients of descent operators on combinatorial Hopf algebras. These
model the breaking-then-recombining of combinational objects. Examples include
the various card-shuffles of Diaconis, Fill and Pitman, Fulman's
restriction-then-induction chains on the representations of the symmetric
group, and a plethora of new chains on trees, partitions and permutations. The
eigenvalues of these chains can be calculated in a uniform manner using Hopf
algebra structure theory, and there is a simple expression for their stationary
distributions. For an important subclass of chains analogous to the
top-to-random shuffle, we derive a full right eigenbasis, from which follow
exact expressions for expectations of certain statistics of interest. This
greatly generalises the coproduct-then-product chains previously studied in
joint work with Persi Diaconis and Arun Ram.

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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th