Disentangling Giant Component and Finite Cluster Contributions in Sparse Matrix Spectra

Abstract

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdos-Renyi graphs as an example and test-bed.

7 pages, 2 multi-part figures

References in corpus (5)

• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Spectra of Sparse Random Matrices
• Cavity approach to the spectral density of non-Hermitian sparse matrices
• Spectrum of Markov generators on sparse random graphs
• Spectra of Random Stochastic Matrices and Relaxation in Complex Systems

Cited by in corpus (8)

• Percolation on complex networks: Theory and application
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Revealing the Micro-Structure of the Giant Component in Random Graph Ensembles
• Large deviation theory for diluted Wishart random matrices
• Localization in random bipartite graphs: numerical and empirical study
• The Fate of Articulation Points and Bredges in Percolation
• A Random Walk Perspective on Hide-and-Seek Games
• Localization properties of the sparse Barrat-Mézard trap model