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A generalization of the carries process

Abstract : We consider a carries process which is a generalization of that by Holte in the sense that (i) we take various digit sets, and (ii) we also consider negative base. Our results are : (i) eigenvalues and eigenvectors of the transition probability matrices, and their connection to combinatorics and representation theory, (ii) an application to the computation of the distribution of the sum of i.i.d. uniform r.v.'s on [0,1], (iii) a relation to riffle shuffle.
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Takahiko Fujita, Fumihiko Nakano, Taizo Sadahiro. A generalization of the carries process. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.61-70. ⟨hal-01207591⟩

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