Local Convergence of Large Critical Multi-type Galton–Watson Trees and Applications to Random Maps
By R. Stephenson. 2014
81 citations recorded by the source corpus.
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.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cbeba1b4b03593e1329cfeb8dda52d70172ec55c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
- Nicolas Curien
- Jean-François Le Gall
- Igor Kortchemski
- C. Abraham
- Douglas Rizzolo
- Amaury Lambert
- Christina Goldschmidt
- Jean Bertoin
In Mathematical Physics
- Nicolas Curien
- Jean-François Le Gall
- Grégory Miermont
- Jérémie Bettinelli
- Igor Kortchemski
- C. Abraham
- Svante Janson
- Douglas Rizzolo
In Statistics and Probability
Citations in the corpus
- The hull process of the Brownian plane (2014, methodology): “A similar invariance principle should hold for the UIPT and for more general random lattices such as the ones constructed by Addario-Berry [2] and Stephenson [32].”