[ΒΙΒΛΙΟ][B] Random trees, Lévy processes and spatial branching processes
T Duquesne, JF Le Gall - 2002 - imo.universite-paris-saclay.fr
The main goal of this work is to investigate the genealogical structure of continuousstate
branching processes in connection with limit theorems for discrete Galton-Watson trees …
branching processes in connection with limit theorems for discrete Galton-Watson trees …
[ΒΙΒΛΙΟ][B] Spatial branching processes, random snakes and partial differential equations
JF Le Gall - 1999 - books.google.com
In these lectures, we give an account of certain recent developments of the theory of spatial
branching processes. These developments lead to several fas cinating probabilistic objects …
branching processes. These developments lead to several fas cinating probabilistic objects …
Branching processes in Lévy processes: the exploration process
The main idea of the present work is to associate with a general continuous branching
process an exploration process that contains the desirable information about the …
process an exploration process that contains the desirable information about the …
A random walk approach to Galton–Watson trees
J Bennies, G Kersting - Journal of theoretical probability, 2000 - Springer
There are several constructions connecting random walks to branching trees. Here we
discuss an approach linking Galton–Watson trees with arbitrary offspring distribution to …
discuss an approach linking Galton–Watson trees with arbitrary offspring distribution to …
On the height profile of a conditioned Galton-Watson tree
G Kersting - arxiv preprint arxiv:1101.3656, 2011 - arxiv.org
Drmota and Gittenberger (1997) proved a conjecture due to Aldous (1991) on the height
profile of a Galton-Watson tree with an offspring distribution of finite variance, conditioned on …
profile of a Galton-Watson tree with an offspring distribution of finite variance, conditioned on …
Random walks on decorated Galton-Watson trees
E Archer - arxiv preprint arxiv:2011.07266, 2020 - arxiv.org
In this article, we study a simple random walk on a decorated Galton-Watson tree, obtained
from a Galton-Watson tree by replacing each vertex of degree $ n $ with an independent …
from a Galton-Watson tree by replacing each vertex of degree $ n $ with an independent …
On maximum family size in branching processes
The number Yn of offspring of the most prolific individual in the nth generation of a Bienaymé–
Galton–Watson process is studied. The asymptotic behaviour of Yn as n→∞ may be viewed …
Galton–Watson process is studied. The asymptotic behaviour of Yn as n→∞ may be viewed …
Random trees, Lévy processes and spatial branching processes
T Duquesne, JFL Gall - arxiv preprint math/0509558, 2005 - arxiv.org
We investigate the genealogical structure of general critical or subcritical continuous-state
branching processes. Analogously to the coding of a discrete tree by its contour function, this …
branching processes. Analogously to the coding of a discrete tree by its contour function, this …
Reduced two-type decomposable critical branching processes with possibly infinite variance
We consider a Galton-Watson process $\mathbf {Z}%(n)=(Z_ {1}(n), Z_ {2}(n)) $ with two
types of particles. Particles of type 2 may produce offspring of both types while particles of …
types of particles. Particles of type 2 may produce offspring of both types while particles of …
Quenched GHP scaling limit of critical percolation clusters on Galton-Watson trees
E Archer, T Lions - arxiv preprint arxiv:2501.12088, 2025 - arxiv.org
We consider quenched critical percolation on a supercritical Galton--Watson tree with either
finite variance or $\alpha $-stable offspring tails for some $\alpha\in (1, 2) $. We show that …
finite variance or $\alpha $-stable offspring tails for some $\alpha\in (1, 2) $. We show that …