By Richard Arratia

The weather of many classical combinatorial constructions could be evidently decomposed into elements. diversifications should be decomposed into cycles, polynomials over a finite box into irreducible components, mappings into attached elements. In all of those examples, and in lots of extra, there are powerful similarities among the numbers of elements of alternative sizes which are present in the decompositions of "typical" components of huge measurement. for example, the complete variety of elements grows logarithmically with the scale of the point, and the dimensions of the most important part is an considerable fraction of the complete. This e-book explains the similarities in asymptotic habit because the results of easy homes shared by way of the constructions: the conditioning relation and the logarithmic situation. The dialogue is carried out within the language of likelihood, permitting the speculation to be built less than fairly common and particular stipulations; for the finer conclusions, Stein's technique emerges because the key factor. The e-book is hence of specific curiosity to graduate scholars and researchers in either combinatorics and likelihood idea. dispensed in the Americas by way of the yank Mathematical Society.

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