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 hα. Defining the total weight for such trees of fixed size to be ZN, a detailed analysis of the analyticity properties of the corresponding generating function is provided. Based on this, we determine the asymptotic form of ZN 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.
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