Probabilistic Limit Theorems Induced by the Zeros of Polynomials
Probability
2023-12-04 v4
Abstract
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry-Esseen bounds, moderate deviation results, concentration inequalities and mod-Gaussian convergence. In addition, an alternate proof of the cumulant bound with improved constants for a class of polynomials all of whose roots lie on the unit circle is provided. A variety of examples is discussed in detail.
Cite
@article{arxiv.2207.08469,
title = {Probabilistic Limit Theorems Induced by the Zeros of Polynomials},
author = {Nils Heerten and Holger Sambale and Christoph Thäle},
journal= {arXiv preprint arXiv:2207.08469},
year = {2023}
}
Comments
Changed in [V2]: Correction of a typo, additional literature added; Changed in [v3]: Thoroughly revised version; Changed in [v4]: additional literature added