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math.PR2026
Power Partitions and Hayman Functions
José L. Fernández, VÃctor J. Maciá
We prove, within the probabilistic framework of Khinchin families, that the generating function of partitions into -th powers is strongly Gaussian in the sense of Báez-Du…
math.PR2026
Uniform integrability of the distance to the nearest leaf in random trees
VÃctor J. Maciá, Benedikt Stufler
We study the distance from the root to the nearest leaf, the analogous quantity for a uniformly chosen vertex, and its protection number, in size-conditioned simply generated trees…
math.PR2025
Some Gaussianity criteria for Khinchin families
VÃctor J. Maciá
In this note we establish simple and verifiable analytical conditions for a power series f in the class K, and its associated Khinchin family, to be Gaussian. We give several momen…