Zooming in at the root of the stable tree

Stable stochastic processes (60G52) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

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Scaling limits of Markov branching trees with applications to Galton-Watson and random unordered trees
The continuum random tree. I
Spinal partitions and invariance under re-rooting of continuum random trees
Behavior near the extinction time in self-similar fragmentations. I: The stable case
Convergence to Lévy stable processes under some weak dependence conditions
Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
A limit theorem for the contour process of conditioned Galton-Watson trees
Self-similar fragmentation derived from the stable tree. I: Splitting at heights
Self-similar fragmentations
The scaling limit of the minimum spanning tree of the complete graph
Probabilistic and fractal aspects of Lévy trees
Self-similar fragmentations derived from the stable tree. II: Splitting at nodes
Cost functionals for large (uniform and simply generated) random trees
Global regime for general additive functionals of conditioned Bienaymé-Galton-Watson trees
Decomposition of Lévy trees along their diameter
The forest associated with the record process on a Lévy tree
Beta-coalescents and continuous stable random trees
Probability and real trees. Ecole d'Eté de Probabilités de Saint-Flour XXXV -- 2005. Lecture given at the Saint-Flour probability summer school, July 6--23, 2005.
Fragmentation processes with an initial mass converging to infinity
A line-breaking construction of the stable trees
Growth of Lévy trees
A Simple Proof of Duquesne’s Theorem on Contour Processes of Conditioned Galton–Watson Trees
Heavy-Tail Phenomena

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