Sampling from the Sherrington-Kirkpatrick model up to β<1/2

A polynomial-time algorithm samples the Sherrington–Kirkpatrick Gibbs distribution with negligible total-variation error for inverse temperatures below one half. The talk combines stochastic localization, Jarzynski's equality and rejection sampling with covariance and functional-inequality estimates. It also derives a weak Poincaré inequality that simplifies the construction and relates the guarantees to earlier Wasserstein results.