LEADER 02856nam 22005175a 450 001 9910151939103321 005 20210304234502.0 010 $a3-03719-500-2 024 70$a10.4171/000 035 $a(CKB)3710000000953784 035 $a(CH-001817-3)15-210304 035 $a(PPN)178152803 035 $a(EXLCZ)993710000000953784 100 $a20210304j20031215 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLogarithmic combinatorial structures: a probabilistic approach$b[electronic resource] /$fRichard Arratia, A. D. Barbour, Simon Tavare? 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2003 215 $a1 online resource (374 pages) 225 0 $aEMS Monographs in Mathematics (EMM) ;$x2523-5192 330 $aThe 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 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. 517 $aLogarithmic Combinatorial Structures 606 $aProbability & statistics$2bicssc 606 $aAlgebra$2bicssc 606 $aNumber theory$2bicssc 606 $aProbability theory and stochastic processes$2msc 606 $aNumber theory$2msc 606 $aField theory and polynomials$2msc 615 07$aProbability & statistics 615 07$aAlgebra 615 07$aNumber theory 615 07$aProbability theory and stochastic processes 615 07$aNumber theory 615 07$aField theory and polynomials 686 $a60-xx$a11-xx$a12-xx$2msc 700 $aArratia$b Richard$0482210 702 $aBarbour$b A. D. 702 $aTavare?$b Simon 801 0$bch0018173 906 $aBOOK 912 $a9910151939103321 996 $aLogarithmic combinatorial structures$9277432 997 $aUNINA