13 problems

In the classical Sherrington–Kirkpatrick model, set $b=0$, let $q$ be a solution of … where $z$ is a standard Gaussian random variable, and let $R_{1,2}$ denote the overlap of two…

Let $F_N(\beta)$ denote the free energy of the Sherrington–Kirkpatrick model with $N$ spins at inverse temperature $\beta$, and let the critical inverse temperature be $\beta_c=1$.…

The Ising $2$-spin Sherrington–Kirkpatrick model is the mean-field spin-glass model with Ising spins and pairwise Gaussian interactions; its overlap distribution describes the law…

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…

Let $\mu_1,\mu_2,\mu_3$ be probability measures with mean $0$ and variance $1$, and let $\Delta(\mu)$ be the discrepancy of a probability measure. Let $\beta(\mu,\infty)$ denote th…

Let $\mu$ be a probability measure with mean $0$ and variance $1$, and define its discrepancy by … Let $\beta(\mu,\infty)$ denote the scaling exponent of the runtime of $\infty$-re…

Let $\mu$ be a “sufficiently nice” probability measure with mean $0$ and variance $1$, and let $\beta(\mu,0)$ denote the scaling exponent of the runtime of $0$-reluctant, or greedy…

Let $\mu$ be a “sufficiently nice” probability measure on $\mathbb{R}$ with $\mathbb{E}_{X \sim \mu}X=0$ and $\mathbb{E}_{X \sim \mu}X^2=1$, let $\lambda\in[0,+\infty]$, and suppos…

For the Sherrington–Kirkpatrick model, let $\beta$ denote the inverse temperature, and let $\beta>\frac{1}{\sqrt{2}}+\eta$, where…

In the Sherrington–Kirkpatrick model on the discrete cube, consider the objective corrected by a generalized TAP correction, under full replica symmetry breaking (fRSB). Subag's ge…

Let $q$ be the Edwards–Anderson parameter … Here $b$ is the transverse-field parameter, and $\beta$ is the inverse temperature. Large-field absence conjecture. For the quantum Sher…

High-temperature Gibbs distribution conjecture. In the high-temperature regime, the Gibbs distribution is somehow close to this conditional annealed measure, which is a complicated…

Disorder chaos conjecture. If $0<t<1$, then the overlap under $G_N'$ takes essentially only one value.