arXiv subjects

Victor Bernal Ramirez

Publications and source records attributed to Victor Bernal Ramirez.

2 recordsLinked to original sources

arXiv2026

Attenuated Poisson Dirichlet approximations for divisibility configurations

We study the point process formed by the normalized logarithms of the distinct prime factors of a harmonic random sample. We prove a quantitative convergence result, in a Wasserstein-type metric over decreasing sequences, toward the atom sequence of a Dickman Poisson cloud conditioned to have total mass at most one, equivalently a uniformly attenuated Poisson-Dirichlet law. The proof is based on the conditioned geometric representation of harmonic samples, a Poisson approximation chain for the associated point processes, monotone couplings of Poisson point processes, and Kolmogorov estimates for the Dickman approximation of weighted geometric sums.

math.PR↗

arXiv2025

Additive functionals of Harmonic samples: the conditioned Dickman regime

We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that, for a broad family of completely additive functions, their evaluations at harmonic samples, suitably normalized, converge in law to conditioned Dickman-type Poisson integrals. This behavior contrasts with the Gaussian limits arising in the classical Erd\"os-Kac theorem under uniform sampling. Our approach combines the probabilistic representation of harmonic samples via independent geometric variables, analytic inputs such as Mertens' approximation, and a Poissonization procedure.

math.NT↗