We prove asymptotic normality of fringe subtrees in random trees with fixed vertex degrees, suggesting new insights into tree structures.
We prove that the number of fringe subtrees, isomorphic to a given tree, in uniformly random trees with given vertex degrees, asymptotically follows a normal distribution. As an application, we establish the same asymptotic normality for random simply generated trees (conditioned Galton-Watson trees). Our approach relies on an extension of Gao and Wormald's (2004) theorem to the multivariate setting.
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Ojeda et al. (2024) studied this question.
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