Rigorous results on the threshold network model

Mathematics – Probability

Scientific paper

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21 pages, Journal of Physics A, in press

Scientific paper

10.1088/0305-4470/38/28/002

We analyze the threshold network model in which a pair of vertices with
random weights are connected by an edge when the summation of the weights
exceeds a threshold. We prove some convergence theorems and central limit
theorems on the vertex degree, degree correlation, and the number of prescribed
subgraphs. We also generalize some results in the spatially extended cases.

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