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