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- W2080498345 abstract "We explain how Itô’s excursion theory can be used to understand the asymptotic behavior of large random trees. We provide precise statements showing that the rescaled contour of a large Galton–Watson tree is asymptotically distributed according to Itô’s excursion measure. As an application, we provide a simple derivation of Aldous’ theorem stating that the rescaled contour function of a Galton–Watson tree conditioned to have a fixed large progeny converges to a normalized Brownian excursion. We also establish a similar result for a Galton–Watson tree conditioned to have a fixed large height." @default.
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- W2080498345 date "2010-05-01" @default.
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- W2080498345 title "Itô’s excursion theory and random trees" @default.
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- W2080498345 doi "https://doi.org/10.1016/j.spa.2010.01.015" @default.
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