Papers & Preprints:

G. Genovese, R. Lucà, R. Montalto, Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map

G. Genovese, Ashkan Nikeghbali, Nicola Serra, Gabriele Visentin, Universal approximation of credit portfolio losses using restricted Boltzmann machines

G. Genovese, Pattern reconstruction with restricted Boltzmann machines (accepted for pubblication in Mathematical Statistics and Learning)

G. Genovese, R. Lucà, N. Tzvetkov, Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs, to appear on Journal d'Analyse Mathématique

G. Genovese, Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines, The Annals of Applied Probability 2023 Vol. 33 No. 3 2324-2341

G. Genovese, A remark on the spherical bipartite spin glass, Mathematical Physics, Analysis and Geometry 25 14 (2022)

G. Genovese, R. Lucà, N. Tzvetkov, Quasi-invariance of Gaussian measures for the periodic Benjamin-Ono-BBM equation, Stochastic and PDEs: Analysis and Computations (2022) 

L. Corsi, G. Genovese, Long time behaviour of a local perturbation in the isotropic XY chain under periodic forcing, Ann. Henri Poincaré 23, 1555-1581 (2022)

G. Genovese, R. Lucà, N. Tzvetkov, Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS, Journal of Functional Analysis 282 (2022) 109263. 

G. Genovese, D. Tantari Legendre Equivalences of Spherical Boltzmann Machines, in Journal Physics A, special issue Machine learning and statistical physics, theory, inspiration, application, Ed. E. Agliari, A. Barra, P. Sollich, L. Zdeborova, 2020. 

G. Genovese, R. Lucà, D. Valeri, Invariant Measures for the Periodic Derivative Nonlinear Schrödinger Equation, Math. Ann. 2019, 374: 1075-1138

G. Genovese, R. Lucà, Local Central Limit Theorem for a Random Walk Perturbed in One Point, Math. Phys. Anal. Geom. 22 19 (2019)

A. Barra, G. Genovese, P. Sollich, D. Tantari, Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Models with Arbitrary Priors, Phys. Rev. E 97, 022310 (2018)

G. Genovese, D. Tantari, Overlap Synchronisation in Multipartite Random Energy Models, J. Stat. Phys. 169: 1162 (2017)

A. Barra, G. Genovese, P. Sollich, D. Tantari, Phase Transitions in Restricted Boltzmann Machines with Generic Priors, Phys. Rev. E 96 042156 (2017)

L. Corsi, G. Genovese, Periodic Driving of an Impurity in the Isotropic XY Chain, Comm. Math. Phys. 35(4), 1173-1203 (2017)

G. Genovese, G. Giacomin, R. L. Greenblatt, Singular behavior of the leading Lyapunov exponent of a product of random 2x2 matrices Comm. Math. Phys. 35(3), 923-958, (2017).

G. Genovese, D. Tantari, Non-Convex Multipartite Ferromagnets, J. Stat. Phys. 163, 492 (2016).

G. Genovese, R. Lucà, D. Valeri, Gibbs Measures Associated to the Integrals of Motion of the Periodic DNLS, Sel. Math. New Ser., 22(3), 1663-1702, (2016).

G. Genovese, D. Tantari, Legendre Duality of Spherical and Gaussian Spin Glasses, Math. Phys. Anal. Geom. 18, 1, (2015).

G. Genovese, On the Dynamics of XY Spin Chains with Impurities, Physica A, 434, 36, (2015).

A. Barra, G. Genovese, F. Guerra, D. Tantari, About a Solvable Mean Field Model of a Gaussian Spin Glass, J. Phys. A: Math. Theor., 47, 155002, (2014).

A. Barra, G. Genovese, F. Guerra, D. Tantari, How Glassy are Neural Networks?, J. Stat. Mech. (2012) P07009.

G. Genovese, S. Simonella, On the Stationary BBGKY Hierarchy for Equilibrium States, J. Stat. Phys. 148, 89, (2012).

G. Genovese, Universality in Bipartite Mean Field Spin Glasses,  J. Math. Phys., 53, 123304, (2012).

A. Barra, G. Genovese, F. Guerra, Equilibrium Statistical Mechanics of Bipartite Spin Systems, J. Phys. A: Math. Theor. 44 245002 (2011).

A. Barra, G. Genovese, F. Guerra, The Replica Symmetric Behaviour of the Analogical Neural Network, J. Stat. Phys. 142, 654, (2010).

G. Gubitosi, G. Genovese, G. Amelino-Camelia, A. Melchiorri, Planck-Scale Modifications to Electrodynamics Characterized by a Space-Like Symmetry-Breaking Vector, Phys. Rev. D 82, 024013 (2010).

G. Genovese, A. Barra, A Certain Class of Curie-Weiss Models, (2009), unpublished.

G. Genovese, A. Barra, A Mechanical Approach to Mean Field Spin Models, J. Math. Phys. 50 (2009).