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• W2995834926 startingPage "065002" @default.
• W2995834926 abstract "We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two orders of the expected eigenvalue spectrum, through the use of infinitely many replica indices taking imaginary values. We apply the method to models in which the spectral constraint reduces to a soft constraint on the number of triangles, which exhibit `shattering' transitions to phases with extensively many disconnected cliques, to models with controlled numbers of triangles and squares, and to models where the spectral constraint reduces to a count of the number of adjacency matrix eigenvalues in a given interval. Our predictions are supported by MCMC simulations based on edge swaps with nontrivial acceptance probabilities." @default.
• W2995834926 created "2019-12-26" @default.
• W2995834926 creator A5010134054 @default.
• W2995834926 creator A5066921728 @default.
• W2995834926 date "2020-01-21" @default.
• W2995834926 modified "2023-09-26" @default.
• W2995834926 title "Imaginary replica analysis of loopy regular random graphs" @default.
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• W2995834926 doi "https://doi.org/10.1088/1751-8121/ab6512" @default.
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