7 problems

Let $G$ be a random $\Delta$-regular graph, and fix an activity parameter $\lambda>0$. The hard-core model on $G$ is the distribution on independent sets $I$ with probability propo…

For the Sherrington–Kirkpatrick model, consider Glauber dynamics for its Gibbs measure in the replica-symmetric regime. Fast-mixing conjecture. Glauber dynamics mixes fast in the r…

The loop algorithm interpolates between the Swendsen–Wang algorithm for classical ferromagnetic Ising Hamiltonians and the operator-loop quantum Monte Carlo algorithm for stoquasti…

Kawasaki dynamics mixing conjecture. For $\beta<\beta_c(\Delta)$, the Kawasaki dynamics mix in time polynomial in $n$ for any fixed magnetization and any graph $G$ of maximum degre…

Let $\Lambda_m^{+}$ be the $d$-dimensional box of side length $m$ equipped with the Ising Glauber dynamics and $+1$ boundary condition. Let the mixing time mean the worst-case tota…

The 3-state Potts model undergoes a first-order phase transition at its critical temperature. The first-order phase transition conjecture. The slow mixing of both the swapping algo…

Let $\pi_{\sigma}$ be a mixture distribution of the form … where $f_{1},\ldots,f_{k}$ are probability densities, $\mu_{1},\ldots,\mu_{k}\geq 0$ are fixed weights satisfying…