Critical Multi-type Galton–Watson Trees Conditioned to be Large

Under minimal condition, we prove the local convergence of a critical multi-type Galton–Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on Z d ....

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Bibliographic Details
Published in:Journal of theoretical probability 2018-06, Vol.31 (2), p.757-788
Main Authors: Abraham, Romain, Delmas, Jean-François, Guo, Hongsong
Format: Article
Language:English
Subjects:
Conditioning
Mathematics
Mathematics and Statistics
Probability
Probability Theory and Stochastic Processes
Progeny
Random walk
Random walk theory
Statistics
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Summary:Under minimal condition, we prove the local convergence of a critical multi-type Galton–Watson tree conditioned on having a large total progeny by types toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on Z d .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-016-0739-8