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 …

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 …

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 study a multi-species spin glass system where the density of each species is kept fixed
at increasing volumes. The model reduces to the Sherrington–Kirkpatrick one for the single …

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 statistical limits of both detecting and estimating a rank-one deformation of a
symmetric random Gaussian tensor. We establish upper and lower bounds on the critical …

The aim of this paper is to give an extensive treatment of bipartite mean field spin systems,
pure and disordered. At first, bipartite ferromagnets are investigated, and an explicit …

Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …

In this paper, we study the high temperature or low connectivity phase of the Viana–Bray
model in the absence of magnetic field. This is a diluted version of the well known …