Random trees : an interplay between combinatorics and probability
Author(s)
Bibliographic Information
Random trees : an interplay between combinatorics and probability
Springer, c2009
Available at / 30 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
DRM||1||1||複本200009118338
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Note
Includes bibliographical references (p. [445]-454) and index
Description and Table of Contents
Description
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.
Table of Contents
Classes of Random Trees.- Generating Functions.- Advanced Tree Counting.- The Shape of Galton-Watson Trees and Polya 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.
by "Nielsen BookData"
