9 papers
A formula for the free energy of non-convex vector spin glasses
Hong-Bin Chen, Fu-Hsuan Ho, Victor Issa
We consider vector mean-field spin glass models with independent and identically distributed spins without assuming the covariance function is convex. We identify the limit free en…
Free energy of non-convex multi-species spin glasses with centered Ising spins
Hong-Bin Chen, Victor Issa, Jean-Christophe Mourrat
We identify the limit free energy of all multi-species spin glasses with centered spins. The result was previously known only under a convexity assumption on the covariance…
Vector spin glasses with Mattis interaction II: non-convex high-temperature models
Hong-Bin Chen, Victor Issa
This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a gene…
Vector spin glasses with Mattis interaction I: the convex case
Hong-Bin Chen, Victor Issa
This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a gener…
The convex structure of the Parisi formula for multi-species spin glasses
Hong-Bin Chen, Victor Issa, Jean-Christophe Mourrat
We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with species, the Parisi formula is known to be valid, and ex…
Uniqueness of Parisi measures for enriched convex vector spin glass
Hong-Bin Chen, Victor Issa
In the PDE approach to mean-field spin glasses, it has been observed that the free energy of convex spin glass models could be enriched by adding an extra parameter in its definiti…
Differentiability and overlap concentration in optimal Bayesian inference
Hong-Bin Chen, Victor Issa
In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by . We show that at every…
A Hopf-like formula for mean-field spin glass models
Victor Issa
We study mean-field spin glass models with general vector spins and convex covariance function. For those models, it is known that the limit of the free energy can be written as th…
Existence and Uniqueness of Permutation-Invariant Optimizers for Parisi Formula
Victor Issa
It has recently been shown in [arXiv:2310.06745] that, upon constraining the system to stay in a balanced state, the Parisi formula for the mean-field Potts model can be written as…