English

Local limit theorem for complex valued sequences

Probability 2025-02-25 v2 Numerical Analysis Numerical Analysis

Abstract

In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of convergence towards an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution.

Keywords

Cite

@article{arxiv.2201.01514,
  title  = {Local limit theorem for complex valued sequences},
  author = {Lucas Coeuret},
  journal= {arXiv preprint arXiv:2201.01514},
  year   = {2025}
}