Edge Flows in the Complete Random-Lengths Network

Mathematics – Probability

Scientific paper

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38 pages, 4 figures

Scientific paper

Consider the complete n-vertex graph whose edge-lengths are independent
exponentially distributed random variables. Simultaneously for each pair of
vertices, put a constant flow between them along the shortest path. Each edge
gets some random total flow. In the $n \to \infty$ limit we find explicitly the
empirical distribution of these edge-flows, suitably normalized.

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