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Sampling and Identity-Testing Without Approximate Tensorization of Entropy
William Gay, William He, Nicholas Kocurek, Ryan O'Donnell
https://arxiv.org/abs/2506.23456

Sampling and Identity-Testing Without Approximate Tensorization of Entropy
Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE distribution mixes fast and can produce approximate samples in a small amount of time, since such a distribution satisfies a modified log-Sobolev inequality. Moreover, identity-testing for an ATE distribution requires few samples if the tester is given coordinat…