Philippe Flajolet and the Airy Function
نویسندگان
چکیده
1. Historical backgrounds: the Airy function in Physics 2 2. The area-Airy distributions: Brownian motion, linear probing hashing, additive parameters in grammars 4 2.1. Area under a Brownian excursion 4 2.2. On the analysis of linear probing hashing 4 2.3. Analytic variations on the Airy distribution 5 2.4. Hachage, arbres, chemins & graphes 6 3. Random matrices, Airy kernel and the Tracy–Widom distributions 6 4. The map-Airy distribution: coalescing saddle points, connectivity in graphs and maps 7 4.1. First cycle in an evolving graph 7 4.2. Random maps, coalescing saddles, singularity analysis, and Airy phenomena 8 4.3. Airy phenomena and analytic combinatorics of connected graphs 9 5. Anecdotes 10
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