Local limits of conditioned Galton-Watson trees: the infinite spine case
By Romain Abraham, Jean-François Delmas. 2013
63 citations recorded by the source corpus.
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d3fc1695f04155449912b48e0f85a5463d82b27c
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Size bias for one and all (2013, background): “A proof can be found in [1], and we now present a more direct proof.”