A considerable number of asymptotic distributions arising in random combinatorics and analysis of algorithms are of the exponential- quadratic type (e−x2), that is, Gaussian. We exhibit here a new class of “universal” phenomena that are of the exponential-cubic type (eix3), corresponding to nonstandard distributions that involve the Airy function. Such Airy phenomena are expected to be found in a number of applications, when confluences of critical points and singularities occur. About a dozen classes of planar maps are treated in this way, leading to the occurrence of a common Airy distribution that describes the sizes of cores and of largest (multi)connected components. Consequences include the analysis and fine optimization of random generation algorithms for multiply connected planar graphs.
CITATION STYLE
Banderier, C., Flajolet, P., Schaeffer, G., & Soria, M. (2000). Planar maps and airy phenomena. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1853, pp. 388–402). Springer Verlag. https://doi.org/10.1007/3-540-45022-x_33
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