30 citations · 171 across the 16 of their papers we have counts for
16 papers
The Invariant Measure of Multiscale Markov Chains via Fast Arborescence Factorization
Diego Alberici, Davide Gabrielli, Giulia Pallotta
We consider a family of continuous-time Markov chains with finite strongly connected transition graph and rates depending on a parameter , so that, when…
Ferromagnetic Ising Model on multiregular random graphs
Diego Alberici, Pierluigi Contucci, Emanuele Mingione +1
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings an…
On the convergence to the non-equilibrium steady state of a Langevin dynamics with widely separated time scales and different temperatures
Diego Alberici, Nicolas Macris, Emanuele Mingione
We study the solution of the two-temperatures Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and…
The solution of the deep Boltzmann machine on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational…
The multi-species mean-field spin-glass on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions…
Deep Boltzmann machines: rigorous results at arbitrary depth
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
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 a -layers…
Annealing and replica-symmetry in Deep Boltzmann Machines
Diego Alberici, Adriano Barra, Pierluigi Contucci +1
In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interac…
Finite-size corrections for the attractive mean-field monomer-dimer model
Diego Alberici, Pierluigi Contucci, Rachele Luzi +1
The finite volume correction for a mean-field monomer-dimer system with an attractive interaction are computed for the pressure density, the monomer density and the susceptibility.…
Two populations mean-field monomer-dimer model
Diego Alberici, Emanuele Mingione
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit…
Mean-Field Monomer-Dimer models. A review
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to cons…
Aggregation models on hypergraphs
Diego Alberici, Pierluigi Contucci, Emanuele Mingione +1
Following a newly introduced approach by Rasetti and Merelli we investigate the possibility to extract topological information about the space where interacting systems are modelle…
Limit theorems for monomer-dimer mean-field models with attractive potential
Diego Alberici, Pierluigi Contucci, Micaela Fedele +1
The number of monomers, in a monomer-dimer mean-field model with an attractive potential, fluctuates according to the central limit theorem when the parameters are outside the crit…
A cluster expansion approach to the Heilmann-Lieb liquid crystal model
Diego Alberici
A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice . Although our choice of the chemical potentials…
A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging…
A mean-field monomer-dimer model with attractive interaction. The exact solution
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb…
Solution of the monomer-dimer model on locally tree-like graphs. Rigorous results
Diego Alberici, Pierluigi Contucci
We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit…