LEADER 05549nam 2200709 450 001 9910830251503321 005 20220609165021.0 010 $a1-280-27276-7 010 $a9786610272761 010 $a0-470-31228-9 010 $a0-471-72215-4 035 $a(CKB)111087027121374 035 $a(EBL)221331 035 $a(OCoLC)475926461 035 $a(SSID)ssj0000227841 035 $a(PQKBManifestationID)11221899 035 $a(PQKBTitleCode)TC0000227841 035 $a(PQKBWorkID)10270162 035 $a(PQKB)11463163 035 $a(MiAaPQ)EBC221331 035 $a(MiAaPQ)EBC5567044 035 $a(Au-PeEL)EBL5567044 035 $a(PPN)152533427 035 $a(EXLCZ)99111087027121374 100 $a20220308d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe probabilistic method /$fNoga Alon, Joel H. Spencer 205 $aSecond edition. 210 1$aNew York :$cInterscience Publishers,$d[2000] 210 4$dİ2000 215 $a1 online resource (322 p.) 225 1 $aWiley-Interscience series in discrete mathematics and optimization 300 $a"A Wiley-Interscience publication." 311 $a0-471-65398-5 311 $a0-471-37046-0 320 $aIncludes bibliographical references (p. 283-293) and indexes. 327 $aDedication; Preface; Acknowledgments; Contents; Part I: METHODS; 1 The Basic Method; 1.1 The Probabilistic Method; 1.2 Graph Theory; 1.3 Combinatorics; 1.4 Combinatorial Number Theory; 1.5 Disjoint Pairs; 1.6 Exercises; The Probabilistic Lens: The Erdo?s-Ko-Rado Theorem; 2 Linearity of Expectation; 2.1 Basics; 2.2 Splitting Graphs; 2.3 Two Quickies; 2.4 Balancing Vectors; 2.5 Unbalancing Lights; 2.6 Without Coin Flips; 2.7 Exercises; The Probabilistic Lens: Bre?gman's Theorem; 3 Alterations; 3.1 Ramsey Numbers; 3.2 Independent Sets; 3.3 Combinatorial Geometry; 3.4 Packing; 3.5 Recoloring 327 $a3.6 Continuous Time3.7 Exercises; The Probabilistic Lens: High Girth and High Chromatic Number; 4 The Second Moment; 4.1 Basics; 4.2 Number Theory; 4.3 More Basics; 4.4 Random Graphs; 4.5 Clique Number; 4.6 Distinct Sums; 4.7 The Ro?dl Nibble; 4.8 Exercises; The Probabilistic Lens: Hamiltonian Paths; 5 The Local Lemma; 5.1 The Lemma; 5.2 Property B and Multicolored Sets of Real Numbers; 5.3 Lower Bounds for Ramsey Numbers; 5.4 A Geometric Result; 5.5 The Linear Arboricity of Graphs; 5.6 Latin Transversals; 5.7 The Algorithmic Aspect; 5.8 Exercises; The Probabilistic Lens: Directed Cycles 327 $a6 Correlation Inequalities6.1 The Four Functions Theorem of Ahlswede and Daykin; 6.2 The FKG Inequality; 6.3 Monotone Properties; 6.4 Linear Extensions of Partially Ordered Sets; 6.5 Exercises; The Probabilistic Lens: Tura?n 's Theorem; 7 Martingales and Tight Concentration; 7.1 Definitions; 7.2 Large Deviations; 7.3 Chromatic Number; 7.4 Two General Settings; 7.5 Four Illustrations; 7.6 Talagrand's Inequality; 7.7 Applications of Talagrand's Inequality; 7.8 Kim-Vu Polynomial Concentration; 7.9 Exercises; The Probabilistic Lens: Weierstrass Approximation Theorem; 8 The Poisson Paradigm 327 $a8.1 The Janson Inequalities8.2 The Proofs; 8.3 Brun's Sieve; 8.4 Large Deviations; 8.5 Counting Extensions; 8.6 Counting Representations; 8.7 Further Inequalities; 8.8 Exercises; The Probabilistic Lens: Local Coloring; 9 Pseudorandomness; 9.1 The Quadratic Residue Tournaments; 9.2 Eigenvalues and Expanders; 9.3 Quasi Random Graphs; 9.4 Exercises; The Probabilistic Lens: Random Walks; Part II: TOPICS; 10 Random Graphs; 10.1 Subgraphs; 10.2 Clique Number; 10.3 Chromatic Number; 10.4 Branching Processes; 10.5 The Giant Component; 10.6 Inside the Phase Transition; 10.7 Zero-One Laws 327 $a10.8 ExercisesThe Probabilistic Lens: Counting Subgraphs; 11 Circuit Complexity; 11.1 Preliminaries; 11.2 Random Restrictions and Bounded-Depth Circuits; 11.3 More on Bounded-Depth Circuits; 11.4 Monotone Circuits; 11.5 Formulae; 11.6 Exercises; The Probabilistic Lens: Maximal Antichains; 12 Discrepancy; 12.1 Basics; 12.2 Six Standard Deviations Suffice; 12.3 Linear and Hereditary Discrepancy; 12.4 Lower Bounds; 12.5 The Beck-Fiala Theorem; 12.6 Exercises; The Probabilistic Lens: Unbalancing Lights; 13 Geometry; 13.1 The Greatest Angle among Points in Euclidean Spaces 327 $a13.2 Empty Triangles Determined by Points in the Plane 330 $aThe leading reference on probabilistic methods in combinatorics-now expanded and updatedWhen it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well 410 0$aWiley-Interscience series in discrete mathematics and optimization. 606 $aCombinatorial analysis 606 $aProbabilities 615 0$aCombinatorial analysis. 615 0$aProbabilities. 676 $a511.6 700 $aAlon$b Noga$066369 702 $aSpencer$b Joel H. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830251503321 996 $aProbabilistic method$9924317 997 $aUNINA