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 …

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse
vol. 46:" Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two …

We present a simple strategy in order to show the existence and uniqueness of the infinite
volume limit of thermodynamic quantities, for a large class of mean field disordered models …

In recent years important progress has been achieved towards proving the validity of the
replica predictions for the (asymptotic) mutual information (or “free energy”) in Bayesian …

The two central topics of information theory are the compression and the transmission of
data. Shannon, in his seminal work, formalized both these problems and determined their …

We consider rank-one non-symmetric tensor estimation and derive simple formulas for the
mutual information. We start by the order 2 problem, namely matrix factorization. We treat it …

The performance of regularized least-squares estimation in noisy compressed sensing is
analyzed in the limit when the dimensions of the measurement matrix grow large. The …

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 …

The motivation that pulls researchers toward spin glasses is possibly not the potential future
use of spin glass materials in “practical” applications. It is rather the expectation that there …