Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Drmota Michael 2004Stochastic analysis of tree–like data structuresProc. R. Soc. Lond. A.460271–307http://doi.org/10.1098/rspa.2003.1243SectionRestricted accessStochastic analysis of tree–like data structures Michael Drmota Michael Drmota Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8–10/118, 1040 Vienna, Austria () Google Scholar Find this author on PubMed Search for more papers by this author Michael Drmota Michael Drmota Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8–10/118, 1040 Vienna, Austria () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 January 2004https://doi.org/10.1098/rspa.2003.1243AbstractThe purpose of this article is to present two types of data structures, binary search trees and usual (combinatorial) binary trees. Although they constitute the same set of (rooted) trees, they are constructed via completely different rules and thus the underlying probabilistic models are different too. Both kinds of data structure can be analysed by probabilistic and stochastic tools, binary search trees (more or less) with martingales and binary trees (which can be considered as a special case of Galton–Watson trees) with stochastic processes. It is also an aim of this article to demonstrate the strength of analytical methods in specific parts of probability theory related to combinatorial problems, and we especially make use of the concept of generating functions. One reason for the use of generating functions is that recursive combinatorial descriptions can be translated to relations for generating functions, and another is that analytical properties of these generating functions can be used to derive asymptotic (probabilistic) relations. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Schwerdtfeger U (2014) Linear functional equations with a catalytic variable and area limit laws for lattice paths and polygons, European Journal of Combinatorics, 10.1016/j.ejc.2013.10.004, 36, (608-640), Online publication date: 1-Feb-2014. SCHWERDTFEGER U, RICHARD C and THATTE B (2010) Area Limit Laws for Symmetry Classes of Staircase Polygons, Combinatorics, Probability and Computing, 10.1017/S0963548309990629, 19:3, (441-461), Online publication date: 1-May-2010. Richard C (2009) On q-functional equations and excursion moments, Discrete Mathematics, 10.1016/j.disc.2007.12.072, 309:1, (207-230), Online publication date: 1-Jan-2009. Cash J (2004) Introduction, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460:2041, (1-8), Online publication date: 8-Jan-2004. Levine L, Lyu H and Pike J (2020) Double Jump Phase Transition in a Soliton Cellular Automaton, International Mathematics Research Notices, 10.1093/imrn/rnaa166 This Issue08 January 2004Volume 460Issue 2041 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1243Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/01/2004Published in print08/01/2004 License: Citations and impact KeywordsHeightBinary Search TreePath LengthGenerating FunctionsProfileBinary Tree