Geodesic
Probabilistic Analysis of Carlitz Compositions
Discrete mathematics & theoretical computer science, Tome 5 (2002).

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Using generating functions and limit theorems, we obtain a stochastic description of Carlitz compositions of large integer n (i.e. compositions two successive parts of which are different). We analyze: the number M of parts, the number of compositions T(m,n) with m parts, the distribution of the last part size, the correlation between two successive parts, leading to a Markov chain. We describe also the associated processes and the limiting trajectories, the width and thickness of a composition. We finally present a typical simulation. The limiting processes are characterized by Brownian Motion and some discrete distributions. 
@article{DMTCS_2002_5_a8,
     author = {Louchard, Guy and Prodinger, Helmut},
     title = {Probabilistic {Analysis} of {Carlitz} {Compositions}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {5},
     year = {2002},
     doi = {10.46298/dmtcs.302},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.302/}
}
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Louchard, Guy; Prodinger, Helmut. Probabilistic Analysis of Carlitz Compositions. Discrete mathematics & theoretical computer science, Tome 5 (2002). doi : 10.46298/dmtcs.302. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.302/

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