Approximating total variation distance between two Gibbs distributions of hardcore or Ising models reduces to sampling and approximate counting, while the same problem for single-vertex marginals is #P-hard even in tractable regimes.
Meel, Dimitrios Myrisiotis, A
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Approximating the total variation distance between spin systems
Approximating total variation distance between two Gibbs distributions of hardcore or Ising models reduces to sampling and approximate counting, while the same problem for single-vertex marginals is #P-hard even in tractable regimes.