02690nam a22004335a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200160018307200160019908400290021510000310024424501390027526000820041430000340049633600260053033700260055633800360058234700240061849000530064250600660069552011410076165000370190265000200193965000260195965000530198565000230203865000380206170000290209970000290212885600320215785600670218915-210304CH-001817-320210304234502.0a fot ||| 0|cr nn mmmmamaa210304e20031215sz fot ||| 0|eng d a978303719500070a10.4171/0002doi ach0018173 7aPBT2bicssc 7aPBF2bicssc 7aPBR2bicssc a60-xxa11-xxa12-xx2msc1 aArratia, Richard,eauthor.10aLogarithmic combinatorial structures: a probabilistic approachh[electronic resource] /cRichard Arratia, A. D. Barbour, Simon TavarÃ©3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2003 a1 online resource (374 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aProbability & statistics2bicssc07aAlgebra2bicssc07aNumber theory2bicssc07aProbability theory and stochastic processes2msc07aNumber theory2msc07aField theory and polynomials2msc1 aBarbour, A. D.,eauthor.1 aTavarÃ©, Simon,eauthor.40uhttps://doi.org/10.4171/000423cover imageuhttps://www.ems-ph.org/img/books/arratia_mini.jpg