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

Abstract

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 ${\bar{d}}_2$-limits of factor of i.i.d. processes are the same.

26 pages; proof of Proposition 9 shortened

References in corpus (4)

• Local algorithms for independent sets are half-optimal
• Independence ratio and random eigenvectors in transitive graphs
• Invariant random matchings in Cayley graphs
• Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy

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