Year: 2006
Type: preprint
Abstract: We prove that critical multitype Galton-Watson trees converge after rescaling to the Brownian continuum random tree, under the hypothesis that the offspring distribution has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees. 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 suitable moment assumptions.
Source: arXiv (Cornell University)
Author: Miermont, Grégory Marc
Institution: Université Paris-Sud
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951900803