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The quadratic step-size scaling conjecture for Metropolis spectral gaps under functional inequalities
Step-size scaling conjecture. The $O(h^4)$ scaling of the spectral gap is merely an artifact of the isoperimetric approach.
Conjectureopenfunctional-inequalities metropolis-algorithms spectral-gaparXiv posted 2 days ago

The quadratic step-size scaling conjecture for Metropolis spectral gaps under functional inequalities