27 citations · 138 across the 20 of their papers we have counts for
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Finite plateau in spectral gap of polychromatic constrained random networks
V. Avetisov, A. Gorsky, S. Nechaev +1
We consider the canonical ensemble of multilayered constrained Erdos-Renyi networks (CERN) and regular random graphs (RRG), where each layer represents graph vertices painted in a…
Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks
V. Avetisov, A. Gorsky, S. Nechaev +1
We have considered an equilibrium ensemble of large Erdős-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly w…
Topological transition in disordered planar matching: combinatorial arcs expansion
Andrey Y. Lokhov, Olga V. Valba, Sergei K. Nechaev +1
In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yield…
New phase transition in random planar diagrams and RNA-type matching
Andrey Y. Lokhov, Sergei K. Nechaev, Mikhail V. Tamm +1
We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values 0 and 1. We show that the existence of a…