Abstract
We consider planar rooted random trees whose distribution is even for fixed height h and size N and whose height dependence is given by a power function . Defining the total weight for such trees of fixed size to be , a detailed analysis of the analyticity properties of the corresponding generating function is provided. Based on this, we determine the asymptotic form of and show that the local limit at large size is identical to the Uniform Infinite Planar Tree, independent of the exponent α of the height distribution function.
Funding Statement
Supported by Villum Fonden via the QMATH Centre of Excellence (Grant no. 10059).
Citation
Bergfinnur Durhuus. Meltem Ünel. "Trees with power-like height dependent weight." Electron. J. Probab. 27 1 - 24, 2022. https://doi.org/10.1214/22-EJP857
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