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- W2160836600 abstract "The N vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the re-scaled by N 2=3 and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reected Brownian motion with drift. Thereby, this work forms the rst example of an inhomogeneous random graph, beyond the case of eectively rank-1 models, which is rigorously shown to be in the Er} os-R enyi graphs universality class in terms of Aldous’s results." @default.
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- W2160836600 date "2014-04-23" @default.
- W2160836600 modified "2023-09-27" @default.
- W2160836600 title "Brownian excursions and critical quantum random graphs" @default.
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