4 papers · 1 filter
On the phase diagram of the multiscale mean-field spin-glass
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione +1
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging…
From entropic constraints to reinforced processes: a probabilistic origin of multiscale measures
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
We investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their c…
Statistical Properties of the Rooted-Tree Encoding of
Pierluigi Contucci, Claudio Giberti, Godwin Osabutey +1
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This…
Limit theorems for the cubic mean-field Ising model
Pierluigi Contucci, Emanuele Mingione, Godwin Osabutey
We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They…