45 citations · 226 across the 20 of their papers we have counts for
22 papers
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 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…
Efficient qubit phase estimation using adaptive measurements
Marco A. Rodríguez-García, Isaac Pérez Castillo, P. Barberis-Blostein
Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology…
Quantum quench in a driven Ising chain
Neil J. Robinson, Isaac Pérez Castillo, Edgar Guzmán-González
We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows ac…
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 exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model
Isaac Pérez Castillo
Inelastic neutron scattering experiments are commonly used to unveil how excitations on Heisenberg spin models play a role in dynamical correlations functions. For a certain class…
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.…
Motion of a Brownian molecule in the presence of reactive boundaries
Arnab Pal, Isaac Pérez Castillo, Anupam Kundu
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understandi…
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…
On the passage properties of the gradual capture of a diffusive particle in the presence of drift
Javier Quetzalcóatl Toledo-Marín, Isaac Pérez Castillo
We investigate a stochastic process consisting of a two-dimensional particle with anisotropic diffusion, mortality rate and a drift velocity, in the presence of an absorbing bounda…
Minimal cooling speed for glass transition in a simple solvable energy landscape model
J. Quetzalcóatl Toledo-Marín, Isaac Pérez Castillo, Gerardo G. Naumis
The minimal cooling speed required to form a glass is obtained for a simple solvable energy landscape model. The model, made from a two-level system modified to include the topolog…
A unified approach for large deviations of bulk and extreme eigenvalues of the Wishart ensemble
Adolfo Camacho Melo, Isaac Pérez Castillo
Within the framework of the Coulomb fluid picture, we present a unified approach to derive the large deviations of bulk and extreme eigenvalues of large Wishart matrices. By analys…
A generalised Airy distribution function for the accumulated area swept by vicious Brownian paths
Isaac Pérez Castillo, Denis Boyer
In this work exact expressions for the distribution function of the accumulated area swept by reunions and meanders of vicious Brownian particles up to time are derived. Th…
Large deviations of the shifted index number in the Gaussian ensemble
Isaac Pérez Castillo
We show that, using the Coulomb fluid approach, we are able to derive a rate function of two variables that captures: (i) the large deviations of bulk eigenvalues; (ii) th…
Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
Isaac Pérez Castillo
We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to comput…
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 Properties of the Jacobi Ensembles via the Coulomb Gas approach
Huda Mohd Ramli, Eytan Katzav, Isaac Pérez Castillo
Using the Coulomb gas method and standard methods of statistical physics, we compute analytically the joint cumulative probability distribution of the extreme eigenvalues of the Ja…
The Storm and Nelson's model for polymer stretching revisited
Francesco A. Massucci, Isaac Pérez Castillo, Conrad Pérez Vicente
The quite recent technological rise in molecular biology allowed single molecule manipulation experiments, where molecule stretching plays a primary role. In order to understand th…
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…
The Little-Hopfield model on a Random Graph
I. Pérez Castillo, N. S. Skantzos
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a…