In this contribution we give a pedagogic introduction to the newly introduced adaptive
interpolation method to prove in a simple and unified way replica formulas for Bayesian …

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 …

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 consider vector spin glasses whose energy function is a Gaussian random field with
covariance given in terms of the matrix of scalar products. For essentially any model in this …

We argue that Hamilton–Jacobi equations provide a convenient and intuitive approach for
studying the large-scale behavior of mean-field disordered systems. This point of view is …

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 …

Statistical inference of finite-rank tensors Page 1 Annales Henri Lebesgue 5 (2022) 1161-1189
HONGBIN CHEN JEAN-CHRISTOPHE MOURRAT JIAMING XIA STATISTICAL INFERENCE …

The Parisi formula is a self-contained description of the infinite-volume limit of the free
energy of mean-field spin glass models. We showthat this quantity can be recast as the …

We give an intrinsic meaning to the Hamilton-Jacobi equation arising from mean-field spin
glass models in the viscosity sense, and establish the corresponding well-posedness …

We propose a simpler approach to identifying the limit of free energy in a vector spin glass
model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the …