The paper characterizes the worst-case query complexity of sampling from smooth non-log-concave distributions as exponential in dimension, with matching lower and upper bounds.
On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
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On the query complexity of sampling from non-log-concave distributions
The paper characterizes the worst-case query complexity of sampling from smooth non-log-concave distributions as exponential in dimension, with matching lower and upper bounds.