Critical Multi-Type Galton-Watson Trees Conditioned to be Large

2015/11/05 by Abraham, Romain, Delmas, Jean-François, Guo, Hongsong
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.01721

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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