On random trees and forests
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.
Affiliations des auteurs :
Alice Contat 1 ; Jean-François Delmas 2 ; Jean-Jil Duchamps 3 ; Igor Kortchemski 4 ; Michel Nassif 2
@article{EP_2023_74_a2,
author = {Alice Contat and Jean-Fran\c{c}ois Delmas and Jean-Jil Duchamps and Igor Kortchemski and Michel Nassif},
title = {On random trees and forests},
journal = {ESAIM. Proceedings},
pages = {19--37},
year = {2023},
volume = {74},
doi = {10.1051/proc/202374019},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202374019/}
}
TY - JOUR AU - Alice Contat AU - Jean-François Delmas AU - Jean-Jil Duchamps AU - Igor Kortchemski AU - Michel Nassif TI - On random trees and forests JO - ESAIM. Proceedings PY - 2023 SP - 19 EP - 37 VL - 74 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202374019/ DO - 10.1051/proc/202374019 LA - en ID - EP_2023_74_a2 ER -
%0 Journal Article %A Alice Contat %A Jean-François Delmas %A Jean-Jil Duchamps %A Igor Kortchemski %A Michel Nassif %T On random trees and forests %J ESAIM. Proceedings %D 2023 %P 19-37 %V 74 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202374019/ %R 10.1051/proc/202374019 %G en %F EP_2023_74_a2
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
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