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Critical multi-type Galton- Watson trees conditioned to be large

Abstract : 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 towards 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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https://hal.archives-ouvertes.fr/hal-01224696
Contributor : Romain Abraham Connect in order to contact the contributor
Submitted on : Monday, September 26, 2016 - 4:56:31 PM
Last modification on : Wednesday, November 3, 2021 - 6:38:42 AM

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Romain Abraham, Jean-François Delmas, Hongsong Guo. Critical multi-type Galton- Watson trees conditioned to be large. Journal of Theoretical Probability, Springer, 2018, pp.757-788. ⟨10.1007/s10959-016-0739-8⟩. ⟨hal-01224696v2⟩

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