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

Published 5 Nov 2015 in math.PR | (1511.01721v2)

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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