Invariance principles for spatial multitype Galton–Watson trees
Miermont, Grégory
Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, p. 1128-1161 / Harvested from Project Euclid
We prove that critical multitype Galton–Watson trees converge after rescaling to the Brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show that the resulting discrete spatial trees converge once suitably rescaled to the Brownian snake, under some moment assumptions.
Publié le : 2008-12-15
Classification:  Multitype Galton–Watson tree,  Discrete snake,  Invariance principle,  Brownian tree,  Brownian snake,  60J80,  60F17
@article{1227287568,
     author = {Miermont, Gr\'egory},
     title = {Invariance principles for spatial multitype Galton--Watson trees},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {44},
     number = {2},
     year = {2008},
     pages = { 1128-1161},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227287568}
}
Miermont, Grégory. Invariance principles for spatial multitype Galton–Watson trees. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp.  1128-1161. http://gdmltest.u-ga.fr/item/1227287568/