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- W3103829863 abstract "We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two phases, a generic phase where the spine becomes infinitely long in the thermodynamic limit and all vertices have finite order and a condensed phase where the spine is finite with probability one and a single vertex of infinite order appears in the thermodynamic limit. We calculate the spectral dimension of the graphs in both phases and prove the existence of a Gibbs measure. We discuss generalizations of this model and the relationship with models of nongeneric random trees." @default.
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- W3103829863 date "2009-11-17" @default.
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- W3103829863 title "Appearance of vertices of infinite order in a model of random trees" @default.
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- W3103829863 doi "https://doi.org/10.1088/1751-8113/42/48/485006" @default.
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