5 papers
Spectral properties and phase diagrams of sparse antagonistic random matrices with diagonal disorder and Jacobian-like structure
Luca Giammanco, Pietro Valigi, Chiara Cammarota
Complex interacting systems are often modelled by random matrices whose spectral properties dictate stability. In sparse antagonistic matrices without diagonal disorder, low connec…
Discontinuous BBP transitions
Dario Bocchi, Giulio Biroli, Chiara Cammarota +1
The Baik-Ben Arous-Peche (BBP) transition sets fundamental limits for detecting low-rank structure in noisy high-dimensional data and underlies a wide range of spectral methods in…
Eigenvalue spectral tails and localization properties of asymmetric networks
Pietro Valigi, Joseph W. Baron, Izaak Neri +2
In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis…
The Role of the Time-Dependent Hessian in High-Dimensional Optimization
Tony Bonnaire, Giulio Biroli, Chiara Cammarota
Gradient descent is commonly used to find minima in rough landscapes, particularly in recent machine learning applications. However, a theoretical understanding of why good solutio…
Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
Andrea Marcello Mambuca, Chiara Cammarota, Izaak Neri
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at mode…