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 ofi.i.d. process on a vertex-transitive infinite graph if and only if it isabsolutely 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 $\bar d_2$-limits of factor of i.i.d. processes are thesame.