Related papers: Random Multi-Overlap Structures for Optimization p…
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…
The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative…
It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product…
We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here…
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…
In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the…
We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural…
In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and…
We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
Bernoulli-$p$ thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences $(X_1,X_2,...)$; (2) gaps of such sequences $(X_{n+1}-X_1)_{n\in\mathbb{N}}$; (3) partition structures. For the first case…
This paper extends recent results on aging in mean field spin glasses on short time scales, obtained by Ben Arous and Gun [2] in law with respect to the environment, to results that hold almost surely, respectively in probability, with…
In the last decades, many efforts have focused on analyzing typical-case hardness in optimization and inference problems. Some recent work has pointed out that polynomial algorithms exist, running with a time that grows more than linearly…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…