45 citations · 226 across the 20 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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 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…