Lifshits Tails for Spectra of Erdős-rényi Random Graphs by Oleksiy Khorunzhiy
نویسنده
چکیده
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectral edge E = 0.
منابع مشابه
Lifshits Tails for Spectra of Erdős-rényi Random Graphs
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
متن کاملLifshitz Tails for Spectra of Erdős–rényi Random Graphs
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshitz-tail behavior at the lower spectra...
متن کاملOn Connected Diagrams and Cumulants of Erdős-Rényi Matrix Models
Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian, we introduce two families of discrete matrix models constructed both with the help of the Erdős-Rényi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of q-step walks and q-step closed walks over the random graph. These sums can be considered as the d...
متن کاملCharacterization of L-norm Statistic for Anomaly Detection in Erdős Rényi Graphs
We devise statistical tests to detect the presence of an embedded ErdősRényi (ER) subgraph inside a random graph, which is also an ER graph. We make use of properties of the asymptotic distribution of eigenvectors of random graphs to detect the subgraph. This problem is related to the planted clique problem that is of considerable interest.
متن کاملMajority-vote on directed Erdős–Rényi random graphs
Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter qc, as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.
متن کامل