Abstract
If T σ 1 T_{\sigma _1} , T σ 2 T_{\sigma _2} are two Gaussian automorphisms, where σ 1 \sigma _1 and σ 2 \sigma _2 are concentrated on independent sets, then we have a dichotomy: either they are spectrally disjoint or they have a common factor. As an application, we construct non-rigid automorphisms which are spectrally determined.
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