Simply Generated Unrooted Plane Trees

Leon Ramzews, Benedikt Stufler
2019 Latin American Journal of Probability and Mathematical Statistics  
We study random unrooted plane trees with n vertices sampled according to the weights corresponding to the vertex-degrees. Our main result shows that if the generating series of the weights has positive radius of convergence, then this model of random trees may be approximated geometrically by a Galton-Watson tree conditioned on having a large random size. This implies that a variety of results for the well-studied planted case also hold for unrooted trees, including Gromov-Hausdorff-Prokhorov
more » ... ausdorff-Prokhorov scaling limits, tail-bounds for the diameter, distributional graph limits, and limits for the maximum degree. Our work complements results by Wang (2016) , who studied random unrooted plane trees whose diameter tends to infinity.
doi:10.30757/alea.v16-12 fatcat:ktf3r74oqjcabg6yt4fdogriyq