Itô's excursion theory and random trees

Jean-François Le Gall

Stochastic Processes and their Applications, 2010, vol. 120, issue 5, 721-749

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.

Keywords: Ito's; excursion; theory; Brownian; excursion; Random; tree; Galton-Watson; tree (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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