Random trees : an interplay between combinatorics and probability

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 o...

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Detalhes bibliográficos
Autor principal: Drmota, Michael, 1964-...., mathématicien
Formato: Livre numérique
Idioma:Anglais
Publicado em: Cham : Springer [20..].
Cham : Springer Nature
Assuntos:
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Nota: Archives Springer e-books (Licence nationale)
Archives Springer e-books (Licence nationale)
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Edition sous un autre format:• Random trees, an interplay between combinatorics and probability, Michael Drmota, 2009, Wien [etc.], Springer, 1 vol. (XVII-458 p.), 978-3-211-75355-2
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245 1 0 |a Random trees :  |b an interplay between combinatorics and probability   |c Michael Drmota. 
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504 |a Bibliogr. p.[443]-454 de l'édition imprimée. Index 
505 1 |a 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 
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520 |a 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 
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