Geodesic
The frequency of pattern occurrence in random walks
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking $n$ data points at evenly-spaced time intervals and mapping them to a length-$n$ permutation determined by relative ordering. The frequency with which certain patterns occur is a useful statistic for such series. However, the behavior of the frequency of pattern occurrence is unstudied for most models. We look at the frequency of pattern occurrence in random walks in discrete time, and we define a natural equivalence relation on permutations under which equivalent patterns appear with equal frequency, regardless of probability distribution. We characterize these equivalence classes applying combinatorial methods. 
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     author = {Elizalde, Sergi and Martinez, Megan},
     title = {The frequency of pattern occurrence in random walks},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     year = {2015},
     doi = {10.46298/dmtcs.2476},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2476/}
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Elizalde, Sergi; Martinez, Megan. The frequency of pattern occurrence in random walks. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2476. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2476/

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