Geodesic
A Central Limit Theorem for Vincular Permutation Patterns
Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2.

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We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem, we use the method of dependency graphs. The main difficulty is then to estimate the variance of our statistics. We need a lower bound on the variance, for which we introduce a recursive technique based on the law of total variance. 
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     author = {Hofer, Lisa},
     title = {A {Central} {Limit} {Theorem} for {Vincular} {Permutation} {Patterns}},
     journal = {Discrete mathematics & theoretical computer science},
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     doi = {10.23638/DMTCS-19-2-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-9/}
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Hofer, Lisa. A Central Limit Theorem for Vincular Permutation Patterns. Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2. doi : 10.23638/DMTCS-19-2-9. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-9/

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