EMS Monographs in Mathematics 2003; 352 pp; hardcover Volume: 1 ISBN10: 3037190000 ISBN13: 9783037190005 List Price: US$79 Member Price: US$63.20 Order Code: EMSMONO/1
 The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of "typical" elements of large size. For instance, the total number of components grows logarithmically with the size of the element, and the size of the largest component is an appreciable fraction of the whole. This book explains the similarities in asymptotic behavior as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient. The book is thus of particular interest to graduate students and researchers in both combinatorics and probability theory. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in probability theory and stochastic processes. Table of Contents  Permutations and primes
 Decomposable combinatorial structures
 Probabilistic preliminaries
 The Ewens sampling formula: methods
 The Ewens sampling formula: asymptotics
 Logarithmic combinatorial structures
 General setting
 Consequences
 A Stein equation
 Point probabilities
 Distributional comparisons with \(P_\theta\)
 Comparisons with \(P_\theta\): point probabilities
 Proofs
 Technical complements
 References
 Notation index
 Author index
 Subject index
