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 …

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 …

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 show that in random K-uniform hypergraphs of constant average degree, for even K≧4,
local algorithms defined as factors of iid can not find nearly maximal cuts, when the average …

The limit free energy of spin-glass models with convex interactions can be represented as a
variational problem involving an explicit functional. Models with non-convex interactions are …

We present the first iterative spectral algorithm to find near-optimal solutions for a random
quadratic objective over the discrete hypercube, resolving a conjecture of Subag [Sub21] …

We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses
with mixed p-spin interactions. The upper bound involves a Guerra-style interpolation and …

We study the Langevin dynamics for spherical pp‐spin models, focusing on the short time
regime described by the Cugliandolo–Kurchan equations. Confirming a prediction of …

We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses.
Our results characterize the maximum value attained by algorithms that are suitably …