Moments of Two-Variable Functions and the Uniqueness of Graph Limits
Combinatorics
2008-12-08 v2 Classical Analysis and ODEs
Abstract
For a symmetric bounded measurable function W on [0,1]^2, "moments" of W can be defined as values t(F,W) indexed by simple graphs. We prove that every such function is determined by its moments up to a measure preserving transformation of the variables. This implies that the limit of a convergent dense graph sequence is unique up to measure preserving transformation.
Cite
@article{arxiv.0803.1244,
title = {Moments of Two-Variable Functions and the Uniqueness of Graph Limits},
author = {Christian Borgs and Jennifer Chayes and Laszlo Lovasz},
journal= {arXiv preprint arXiv:0803.1244},
year = {2008}
}
Comments
29 pages