Geodesic
Extremal Statistics on Non-Crossing Configurations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We obtain several properties of extremal statistics in non-crossing configurations with n vertices. We prove that the maximum degree and the largest component are of logarithmic order, and the diameter is of order $\sqrt{n}$. The proofs are based on singularity analysis, an application of the first and second moment method and on the analysis of iterated functions. 
@article{DMTCS_2012_special_263_a55,
     author = {Mier, Anna and Noy, Marc},
     title = {Extremal {Statistics} on {Non-Crossing} {Configurations}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3069/}
}
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%V DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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Mier, Anna; Noy, Marc. Extremal Statistics on Non-Crossing Configurations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3069. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3069/

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