Local Convergence of Large Critical Multi-type Galton–Watson Trees and Applications to Random Maps

Robin Stephenson ()
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Robin Stephenson: Universität Zürich

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 159-205

Abstract: Abstract 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 type, 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.

Keywords: Galton–Watson processes; Random trees; Random maps; Local convergence; 05C63; 05C80; 05C81; 60B10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-016-0707-3

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