7 papers
Wiman-Valiron inequalities in the unit disk outside sets of finite logarithmic measure
Víctor J. Maciá
We give affirmative answers to both parts of Question 2.6 posed by Grosse-Erdmann (2025) concerning Wiman-Valiron inequalities in the unit disk. For every unbounded analytic functi…
Limit laws of random simplex tree-child networks
Víctor J. Maciá, Benedikt Stufler
We prove that the longer and shorter Sackin indices of a uniformly random simplex tree-child network with taxa admit joint distributional limits after rescaling by .…
Uniform integrability of the distance to the nearest leaf in random trees
Víctor 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…
Power Partitions and Hayman Functions
José L. Fernández, Víctor 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-Dua…
Galton-Watson processes, simple varieties of trees and Khinchin families
Víctor J. Maciá
In this note, we introduce a unified analytic framework that connects simple varieties of trees, Bienayme-Galton-Watson processes and Khinchin families. Using Lagrange's inversion…
The Theory of Khinchin Families
Víctor J. Maciá
The theory of Khinchin families connects Probability Theory and Complex Analysis. Along this PhD thesis, we exploit this connection to obtain, using a variety of local central limi…
Some Gaussianity criteria for Khinchin families
Víctor 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…