Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.
Bernoulli shifts with the same entropy are isomorphic.Advances in Mathematics, 4(3):337–352, 1970
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Graph Disjointness with Applications to Reversible Markov Chains
Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.