Spectral measures of factor of i.i.d. processes on vertex-transitive graphs
Probability
2021-03-23 v2
Abstract
We prove that a measure on is the spectral measure of a factor of i.i.d. process on a vertex-transitive infinite graph if and only if it is absolutely continuous with respect to the spectral measure of the graph. Moreover, we show that the set of spectral measures of factor of i.i.d. processes and that of -limits of factor of i.i.d. processes are the same.
Keywords
Cite
@article{arxiv.1505.07412,
title = {Spectral measures of factor of i.i.d. processes on vertex-transitive graphs},
author = {Ágnes Backhausz and Bálint Virág},
journal= {arXiv preprint arXiv:1505.07412},
year = {2021}
}
Comments
26 pages; proof of Proposition 9 shortened