Thinning Operation via the Poisson-Föllmer Process

Ioannis Kavvadias

Thinning Operation via the Poisson-Föllmer Process

Probability 2026-08-03 v1 Information Theory

Authors: Ioannis Kavvadias

Abstract

We give an alternative proof of Yu's Thinning Lemma and of the Law of Thin Numbers using a stochastic variational formula for the relative entropy. We show that this approach yields new convergence rates for the Law of Thin Numbers, complementing and extending previously known results.

Keywords

thinning operation Poisson-Föllmer process Law of Thin Numbers relative entropy stochastic variational formula convergence rates

Cite

@article{arxiv.2608.02927,
  title  = {Thinning Operation via the Poisson-Föllmer Process},
  author = {Ioannis Kavvadias},
  journal= {arXiv preprint arXiv:2608.02927},
  year   = {2026}
}