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 …

By using a simple interpolation argument, in previous work we have proven the existence of
the thermodynamic limit, for mean field disordered models, including the Sherrington …

The Parisi Formula Page 1 Annals of Mathematics, 163 (2006), 221-263 The Parisi formula By
Michel Talagrand* Dedicated to Francesco Guerra Abstract Using Guerra's interpolation …

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy
of the Sherrington-Kirkpatrick (SK) spin-glass model could have been taken as offering …

Abstract The authors of [Ann. Henri Poincaré 16 (2015) 691–708] introduced a multi-species
version of the Sherrington–Kirkpatrick model and suggested the analogue of the Parisi …

We study the Ising pure $ p $-spin model for large $ p $. We investigate the landscape of the
Hamiltonian of this model. We show that for any $\gamma> 0$ and any large enough $ p …

The Wigner spiked model in a mismatched setting is studied with the finite temperature
Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick …

A class of deep Boltzmann machines is considered in the simplified framework of a
quenched system with Gaussian noise and independent entries. The quenched pressure of …

In this work we present a rigorous and straightforward method to detect the onset of the
instability of replica-symmetric theories in information processing systems, which does not …