Spectral measures of factor of i.i.d. processes on vertex-transitive graphs

摘要

We prove that a measure on [-d, d] 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 (d) over bar (2)- limits of factor of i.i.d. processes are the same.