Random Trees: An Interplay between Combinatorics and Probability by Michael DrmotaRandom Trees: An Interplay between Combinatorics and Probability by Michael Drmota

Random Trees: An Interplay between Combinatorics and Probability

byMichael Drmota

Paperback | October 13, 2010

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Trees are a fundamental object in graph theory and combinatorics as well as a basic object for data structures and algorithms in computer science. During thelastyearsresearchrelatedto(random)treeshasbeenconstantlyincreasing and several asymptotic and probabilistic techniques have been developed in order to describe characteristics of interest of large trees in di?erent settings. Thepurposeofthisbookistoprovideathoroughintroductionintovarious aspects of trees in randomsettings anda systematic treatment ofthe involved mathematicaltechniques. It shouldserveasa referencebookaswellasa basis for future research. One major conceptual aspect is to connect combinatorial and probabilistic methods that range from counting techniques (generating functions, bijections) over asymptotic methods (singularity analysis, saddle point techniques) to various sophisticated techniques in asymptotic probab- ity (convergence of stochastic processes, martingales). However, the reading of the book requires just basic knowledge in combinatorics, complex analysis, functional analysis and probability theory of master degree level. It is also part of concept of the book to provide full proofs of the major results even if they are technically involved and lengthy.
Title:Random Trees: An Interplay between Combinatorics and ProbabilityFormat:PaperbackDimensions:458 pages, 23.5 × 15.5 × 0.17 inPublished:October 13, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3211999140

ISBN - 13:9783211999141


Table of Contents

Classes of Random Trees.- Generating Functions.- Advanced Tree Counting.- The Shape of Galton-Watson Trees and Pólya Trees.- The Vertical Profile of Trees.- Recursive Trees and Binary Search Trees.- Tries and Digital Search Trees.- Recursive Algorithms and the Contraction Method.- Planar Graphs.