Geodesic
On random trees and forests
Alice Contat1 ; Jean-François Delmas2 ; Jean-Jil Duchamps3 ; Igor Kortchemski4 ; Michel Nassif2
1 Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France
2 CERMICS, Ecole des Ponts, France
3 LmB, UMR 6623, Université Bourgogne Franche-Comté, CNRS, F-25000 Besançon, France
4 CMAP, École Polytechnique, 91128 Palaiseau CEDEX, France
ESAIM. Proceedings, Tome 74 (2023), pp. 19-37.

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The first talk at the session Random trees and random forests “Journée MAS” (27/08/2021) was presented by I. Kortchemski. After a general up-to-date introduction to local and scaling limits of Bienaymé trees (which are discrete branching trees), he presented new results on precise behavior of the largest out-degree of large branching trees when the offspring distribution μ is subcritical with μ(n) of order n−β for large n and β > 2 or critical with μ(n) of order n−2. In the next talk, M. Nassif gave asymptotics of additive functionals of large Bienayme trees in the global regime, which can be understood using scaling limits. Looking at Cayley trees with fixed size, A. Contat established a surprising identity for randomly built independent sets. Eventually J.-J. Duchamps presented some results on the distribution of the discrete Moran forest, a random graph arising in a classical population model at equilibrium.
DOI : 10.1051/proc/202374019

Alice Contat 1 ; Jean-François Delmas 2 ; Jean-Jil Duchamps 3 ; Igor Kortchemski 4 ; Michel Nassif 2

1 Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France
2 CERMICS, Ecole des Ponts, France
3 LmB, UMR 6623, Université Bourgogne Franche-Comté, CNRS, F-25000 Besançon, France
4 CMAP, École Polytechnique, 91128 Palaiseau CEDEX, France 
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Alice Contat; Jean-François Delmas; Jean-Jil Duchamps; Igor Kortchemski; Michel Nassif. On random trees and forests. ESAIM. Proceedings, Tome 74 (2023), pp. 19-37. doi : 10.1051/proc/202374019. http://geodesic.mathdoc.fr/articles/10.1051/proc/202374019/

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