Logarithmic Combinatorial Structures: A Probabilistic Approach
European Mathematical Society, 2003 - Asympotic distribution (Probability theory) - 363 pages
"This book explains the similarities in asymptotic behaviour 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." --Book Jacket.
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Permutations and Primes
Decomposable Combinatorial Structures
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analog applied approximation argument Arratia and Tavare assemblies asymptotic Barbour and Tavare bounded central limit theorem Chapter completing the proof compound Poisson distribution Conditioning Relation Conditions Aq converges in distribution Corollary 10.3 Corollary 4.8 corresponding defined denote elements error Ewens Sampling Formula example F[Tbn F[Tbn(Z F[Tvm(Z Feller coupling finite follows given gives Hence hold i=b+l i=v+l implies independent random variables inequality integer j=b+l joint distribution large components LLTa logarithmic combinatorial structures logn multisets multisets and selections number of cycles point probabilities Poisson distribution Poisson process Poisson random variables Poisson-Dirichlet prime factors probability space proof of Theorem proved random mappings random permutations Remark result satisfying the Logarithmic scale invariant sequence small components square free polynomials Stein Equation Stein's method Theorem 7.7 total variation distance Tvm(Z uniformly values Wasserstein distance