Abstract
The Harris correspondence between random walks and random trees, reviewed in Section 6.3, suggests that a continuous path be regarded as encoding some kind of infinite tree, with each upward excursion of the path corresponding to a subtree. This idea has been developed and applied in various ways by Neveu- Pitman [324, 323], Aldous [5, 6, 7] and Le Gall [271, 272, 273, 275]. This chapter reviews this circle of ideas, with emphasis on how the Brownian forest can be grown to explore finer and finer oscillations of the Brownian path, and how this forest growth process is related to Williams’ path decompositions of Brownian motion at the time of a maximum or minimum.
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© 2006 Springer-Verlag Berlin/Heidelberg
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Pitman, J. (2006). The Brownian forest. In: Picard, J. (eds) Combinatorial Stochastic Processes. Lecture Notes in Mathematics, vol 1875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34266-4_8
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DOI: https://doi.org/10.1007/3-540-34266-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30990-1
Online ISBN: 978-3-540-34266-3
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