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 .

References in corpus (2)

• Condensation in nongeneric trees
• Conditioning Galton-Watson trees on large maximal out-degree

Cited by in corpus (1)

• On scaling limits of multitype Galton-Watson trees with possibly infinite variance