We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no
external field, and study the problem of sampling from the Gibbs distribution μ in polynomial …

Let A∈\mathbbR^n*n be a symmetric random matrix with independent and identically
distributed (iid) Gaussian entries above the diagonal. We consider the problem of …

We study the problem of algorithmically optimizing the Hamiltonian HN H_N of a spherical or
Ising mixed pp‐spin glass. The maximum asymptotic value OPT OPT of HN/N H_N/N is …

We establish the satisfiability threshold for random k-SAT for all k≥ k0. That is, there exists a
limiting density αs (k) such that a random k-SAT formula of clause density α is with high …

Optimization of mean-field spin glasses Page 1 The Annals of Probability 2021, Vol. 49, No. 6,
2922–2960 https://doi.org/10.1214/21-AOP1519 © Institute of Mathematical Statistics, 2021 …

The Potts spin glass is a generalization of the Sherrington–Kirkpatrick (SK) model that
allows for spins to take more than two values. Based on a novel synchronization …

For Erdős–Rényi random graphs with average degree γ, and uniformly random γ-regular
graph on n vertices, we prove that with high probability the size of both the Max-Cut and …

We consider the power of local algorithms for approximately solving Max $ k $ XOR, a
generalization of two constraint satisfaction problems previously studied with classical and …

We consider Ising mixed $ p $-spin glasses at high-temperature and without external field,
and study the problem of sampling from the Gibbs distribution $\mu $ in polynomial time. We …

We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …