English

How complex is a random picture?

Probability 2020-02-07 v1

Abstract

We study the amount of information that is contained in "random pictures", by which we mean the sample sets of a Boolean model. To quantify the notion "amount of information", two closely connected questions are investigated: on the one hand, we study the probability that a large number of balls is needed for a full reconstruction of a Boolean model sample set. On the other hand, we study the quantization error of the Boolean model w.r.t. the Hausdorff distance as a distortion measure.

Keywords

Cite

@article{arxiv.1806.06597,
  title  = {How complex is a random picture?},
  author = {Frank Aurzada and Mikhail Lifshits},
  journal= {arXiv preprint arXiv:1806.06597},
  year   = {2020}
}

Comments

39 pages

R2 v1 2026-06-23T02:32:57.756Z