Related papers: Solving the fully-connected spherical $p$-spin mod…
In this three-sections lecture cavity method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetric (RS) and 1-step replica symmetry breaking…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
Purpose of this paper is to face up to P-spin glass and Gaussian P-spin model, i.e. spin glasses with polynomial interactions of degree P > 2. We consider the replica symmetry and first step of replica simmetry breaking assumptions and we…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
We study $p$-spin glass models on regular random graphs. By analyzing the Franz-Parisi potential with a two-body cavity field approximation under the replica symmetric ansatz, we obtain a good approximation of the 1RSB transition…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs,…
Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the…
Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…
We study a large-$N$ bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the $p$-spin spherical model. Replica symmetry is broken at low temperatures and for…
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass…
We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any…
This paper investigates p-spin distributions for a generic spherical p-spin model; we give a representation of spin distributions in terms of a stochastic process. In order to do this, we find a novel double limit scheme that allows us to…
Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor…
We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in…
We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the…
The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one…
We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…