Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
Jacques Neveu, Jim Pitman (1989)
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Jacques Neveu, Jim Pitman (1989)
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We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning...