45 citations · 226 across the 20 of their papers we have counts for
8 papers · 1 filter
Spectral Signatures of Replica Symmetry Breaking in Optimization-Induced Random Matrices
Isaac Pérez Castillo
We study optimization-induced matrix ensembles generated by Gibbs measures. The same quenched disorder that weights configurations also supplies the matrix entries observed on them…
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…
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…
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.…
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…
Spectral density of products of Wishart dilute random matrices. Part I: the dense case
Thomas Dupic, Isaac Pérez Castillo
In this work we study the spectral density of products of Wishart diluted random matrices of the form using the Edwards-Jones trick to map this…
Spectral density of random graphs with topological constraints
Tim Rogers, Conrad Pérez Vicente, Koujin Takeda +1
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlation…
On exact mappings between fermionic Ising spin glass and classical spin glass models
Isaac Pérez Castillo, David Sherrington
We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard i…