Arbres et marches aléatoires

Kortchemski, Igor

doi:10.5802/xups.2016-01

Kortchemski, Igor ¹

¹ CNRS & CMAP, École polytechnique, Université Paris-Saclay

Journées mathématiques X-UPS, Arbres et marches aléatoires (2016), pp. 1-57.

Résumé

Nous nous intéressons à de grands arbres aléatoires qui décrivent la généalogie d’une population se reproduisant de manière asexuée. Ce modèle a été introduit à la fin du xix^e siècle par Bienaymé et Galton & Watson pour prédire l’extinction des noms nobles en Angleterre. En n’utilisant essentiellement que des outils au programme des classes préparatoires scientifiques, nous étudions la géométrie de ces arbres en les codant par des marches aléatoires conditionnées, que nous analysons à leur tour en utilisant des arguments combinatoires et analytiques.

Publié le : 2024-08-06

DOI : 10.5802/xups.2016-01

Affiliations des auteurs :

Kortchemski, Igor ¹

¹ CNRS & CMAP, École polytechnique, Université Paris-Saclay

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Kortchemski, Igor. Arbres et marches aléatoires. Journées mathématiques X-UPS, Arbres et marches aléatoires (2016), pp. 1-57. doi : 10.5802/xups.2016-01. http://www.numdam.org/articles/10.5802/xups.2016-01/

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