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.
- ISBN10 3211101780
- ISBN13 9783211101780
- Publish Date 6 June 2009 (first published 22 December 2008)
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 478
- Language English