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

Romain Abraham (), Jean-François Delmas () and Hongsong Guo ()
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Romain Abraham: Université d’Orléans
Jean-François Delmas: Université Paris-Est, CERMICS (ENPC)
Hongsong Guo: Université Paris-Est, CERMICS (ENPC)

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 757-788

Abstract: 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 toward a multi-type Kesten’s tree. We obtain the result by generalizing Neveu’s strong ratio limit theorem for aperiodic random walks on $$\mathbb {Z}^d$$ Z d .

Keywords: Galton–Watson tree; Random tree; Local limit; Strong ratio theorem; Branching process; 60J80; 60B10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-016-0739-8

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