title: Eigenvalue tunneling and decay of quenched random network.
abstract: We consider the canonical ensemble of N-vertex Erdős-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity μ for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p^{-1}] almost full subgraphs (cliques) above critical fugacity, μ_{c}, where p is the ER bond formation probability. Evolution of the spectral density, ρ(λ), of the adjacency matrix with increasing μ leads to the formation of a multizonal support for μ>μ_{c}. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.
authors.affiliation: N. N. Semenov Institute of Chemical Physics of the Russian Academy of Sciences, 119991 Moscow, Russia.|Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia.
authors.forename: V
authors.initials: V
authors.lastname: Avetisov
authors.affiliation: Chair of Programming and Information Technologies, Yerevan State University, Yerevan, Armenia.
authors.forename: M
authors.initials: M
authors.lastname: Hovhannisyan
authors.affiliation: Institute of Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia.|Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia.
authors.forename: A
authors.initials: A
authors.lastname: Gorsky
authors.affiliation: Poncelet Laboratory, Centre National de la Recherche Scientifique (UMI2615), Independent University of Moscow, Moscow, Russia.|P. N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia.
authors.forename: S
authors.initials: S
authors.lastname: Nechaev
authors.affiliation: Physics Department, Moscow State University, 119992 Moscow, Russia.|Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia.
authors.forename: M
authors.initials: M
authors.lastname: Tamm
authors.affiliation: N. N. Semenov Institute of Chemical Physics of the Russian Academy of Sciences, 119991 Moscow, Russia.|Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia.
authors.forename: O
authors.initials: O
authors.lastname: Valba