We introduce a weighted model of random trees and analyze the asymptotic properties of their heights. Our framework encompasses most trees of logarithmic height that were introduced in the context of the analysis of algorithms or combinatorics. This allows us to state a sort of "master theorem" for the height of random trees, that covers binary search trees (Devroye, 1986), random recursive trees (Devroye, 1987; Pittel, 1994), digital search trees (Pittel, 1985), scale-free trees (Pittel, 1994; Barabasi and Albert, 1999), and all polynomial families of increasing trees (Bergeron et al., 1992; Broutin et al., 2006) among others. Other applications include the shape of skinny cells in geometric structures like k-d and relaxed k-d trees. / This new approach sheds new light on the tight relationship between data structures like trees and tries that used to be studied separately. In particular, we show that digital search trees and the tries built from sequences generated by the same memoryless source share the same stable core. This link between digital search trees and tries is at the heart of our analysis of heights of tries. It permits us to derive the height of several species of tries such as the trees introduced by de la Briandais (1959) and the ternary search trees of Bentley and Sedgewick (1997). / The proofs are based on the theory of large deviations. The first order terms of the asymptotic expansions of the heights are geometrically characterized using the Crame'r functions appearing in estimates of the tail probabilities for sums of independent random variables.

Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Licentiatavhandling Uppsala, Univ : 2004.

Thesis (Ph. D.) - University of Washington. / Bibliography: ℓ.[184]-185.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 98-103). Also available in electronic version.

Thesis (Honors)--College of William and Mary, 2008. / Includes bibliographical references (leaf 39). Also available via the World Wide Web.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Embeddings; graph theory; pseudo-triangulations. Includes bibliographical references (leaves 30-31).

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains vi, 49 p. : ill. Includes abstract. Includes bibliographical references (p. 47-49).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Dual Eulerian Graphs; VLSI. Includes bibliographical references (p. 170-171).

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 114-117).