We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analogous to Kesten's infinite monotype Galton-Watson tree.
This is proven when we condition on the number of vertices of one fixed types, and with an extra technical assumption if we count at least two types. We then apply these results to study local limits of random planar maps, showing that large critical Boltzmann-distributed random maps converge in distribution to an infinite map.
Biography
Robin Stephenson is a postdoc at NYU Shanghai. He obtained his Ph.D. at Paris Dauphine University, supervised by Bénédicte Haas and Grégory Miermont. He was also a postdoc at the University of Zürich, in Jean Bertoin's group. His research interests include random trees, random maps and fragmentation-type processes.