Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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Expected supremum of canonical processes with log-concave tails is equivalent up to universal constants to a functional on parameterized separation trees, with a polynomial-time approximation algorithm for finite cases.
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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The Dual Majorizing Measure Theorem for Canonical Processes
Expected supremum of canonical processes with log-concave tails is equivalent up to universal constants to a functional on parameterized separation trees, with a polynomial-time approximation algorithm for finite cases.