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 …

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 …

The goal of this book is to present new mathematical techniques for studying the behaviour
of mean-field systems with disordered interactions. We mostly focus on certain problems of …

We study the vector spin generalization of the ℓ p-Gaussian-Grothendieck problem. In other
words, given integer κ≥ 1, we investigate the asymptotic behaviour of the ground state …

Given an $ n\times n $ matrix $ A_n $ and $1\leq r, p\leq\infty $, consider the following
quadratic optimization problem referred to as the $\ell_r $-Grothendieck problem:\begin …

We prove the free energy and ground state energy of spherical spin glasses are universal
under the minimal moment assumptions. Previously such universality was known only for …

We consider the Ising Curie-Weiss model on the complete graph constrained under a given
$\ell^{p} $ norm for some $ p> 0$. For $ p=\infty $, it reduces to the classical Ising Curie …

Motivated by the general matrix deviation inequality for iid ensemble Gaussian matrix [R.
Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science …

Motivated by the general matrix deviation inequality for iid ensemble Gaussian matrix, we
study its universality property. As a starting point for this problem, we show that this property …