Improved mixing time for Markov chains on statistical physics model.
Thuy-Duong Vuong, UC Berkeley
Abstract: In this talk, I will discuss recent progress on bounding the mixing time of Markov chains to sample from spin systems from statistical physics. For example, for the Sherrington-Kirkpatrick (SK) Ising model, we show the optimal quasi-linear mixing time up to the current-best temperature threshold of β= 0.295 [AKV24], improving upon the previous best bound of β = 0.25 [AJKPV21, CE22]. The recent spectral/entropic independence framework [ALO’20, CLV21-22, CFYZ21-22, AJKPV21-24, CE22] controls the mixing time of Markov chains using spectral bounds on the covariance of the stationary distribution. Our new result for the SK Ising model relies upon a new bound for this covariance matrix by generalizing Oppenheim’s trickle-down to linear-tilt localization schemes. Based on joint work with Nima Anari, Vishesh Jain, Frederic Koehler, and Huy Tuan Pham.
