The cut metric for probability distributions
Combinatorics
2020-12-02 v2 Discrete Mathematics
Mathematical Physics
math.MP
Probability
Abstract
Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called {\em pinning} on the space of limit objects and show how this operation yields a canonical cut metric approximation to a given probability distribution akin to the weak regularity lemma for graphons. We also establish the cut metric continuity of basic operations such as taking product measures.
Cite
@article{arxiv.1905.13619,
title = {The cut metric for probability distributions},
author = {Amin Coja-Oghlan and Max Hahn-Klimroth},
journal= {arXiv preprint arXiv:1905.13619},
year = {2020}
}