79 citations · 583 across the 34 of their papers we have counts for
35 papers
Epidemic threshold and localization of the SIS model on directed complex networks
Vinícius B. Müller, Fernando L. Metz
We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory wit…
Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
Leonardo Ferreira, Fernando Metz, Paolo Barucca
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained b…
Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
Jeferson D. da Silva, Diego Tapias, Peter Sollich +1
We study the spectral properties and eigenvector statistics of the Laplacian on highly-connected networks with random coupling strengths and a gamma distribution of rescaled degree…
Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
Fernando L. Metz
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interac…
Effects of clustering heterogeneity on the spectral density of sparse networks
Tuan Minh Pham, Thomas Peron, Fernando L. Metz
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a…
Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise
Leonardo S. Ferreira, Fernando L. Metz
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the I…
Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties
Jeferson D. Silva, Fernando L. Metz
The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment.…
Mean-field theory of vector spin models on networks with arbitrary degree distributions
Fernando L. Metz, Thomas Peron
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-fi…
Analytic solution of the two-star model with correlated degrees
Maíra Bolfe, Fernando L. Metz, Edgar Guzmán-González +1
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime…
Analytic approach for the number statistics of non-Hermitian random matrices
Antonio Tonatiúh Ramos Sánchez, Edgar Guzmán-González, Isaac Pérez Castillo +1
We introduce a powerful analytic method to study the statistics of the number of eigenvalues inside any contour for infinitely large…
The spectral density of dense random networks and the breakdown of the Wigner semicircle law
Fernando L. Metz, Jeferson D. Silva
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By con…
Localization and universality of eigenvectors in directed random graphs
Fernando L. Metz, Izaak Neri
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an e…
Superextreme Waves Generation in the Linear Regime
Cristian Bonatto, Sandra D. Prado, Fernando L. Metz +3
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear…
Phase transitions in atypical systems induced by a condensation transition on graphs
Edgar Guzmán-González, Isaac Pérez Castillo, Fernando L. Metz
Random graphs undergo structural phase transitions that are crucial for dynamical processes and cooperative behavior of models defined on graphs. In this work we investigate the im…
Linear stability analysis for large dynamical systems on directed random graphs
Izaak Neri, Fernando Lucas Metz
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegre…
Condensation of degrees emerging through a first-order phase transition in classical random graphs
Fernando L. Metz, Isaac Pérez Castillo
Due to their conceptual and mathematical simplicity, Erdös-Rényi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas.…
Phase diagram and metastability of the Ising model on two coupled networks
Maíra Bolfe, Lucas Nicolao, Fernando L. Metz
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erdös…
Theory for the conditioned spectral density of non-invariant random matrices
Isaac Pérez Castillo, Fernando L. Metz
We develop a theoretical approach to compute the conditioned spectral density of non-invariant random matrices in the limit . This large deviatio…
Large deviation theory for diluted Wishart random matrices
Isaac Pérez Castillo, Fernando L. Metz
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we de…
Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
Fernando L. Metz, Isaac Pérez Castillo
We calculate the level compressibility of the energy levels inside for the Anderson model on infinitely large random regular graphs with on-site potentials di…
Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
Izaak Neri, Fernando Lucas Metz
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they de…
Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
Fernando L. Metz, Isaac Pérez Castillo
We present a general method to obtain the exact rate function controlling the large deviation probability $\text{Prob}[\mathcal{I}_N[a,b]=kN] \asymp e^{-NΨ_{[a,b]}(k…
Replica-symmetric approach to the typical eigenvalue fluctuations of Gaussian random matrices
Fernando L. Metz
We discuss an approach to compute the first and second moments of the number of eigenvalues that lie in an arbitrary interval of the real line for Gaussian rando…
Statistical mechanics of the spherical hierarchical model with random fields
Fernando L. Metz, Jacopo Rocchi, Pierfrancesco Urbani
We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagneti…