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The probabilistic method / / Noga Alon, Joel H. Spencer
| The probabilistic method / / Noga Alon, Joel H. Spencer |
| Autore | Alon Noga |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New York : , : Interscience Publishers, , [2000] |
| Descrizione fisica | 1 online resource (322 p.) |
| Disciplina | 511.6 |
| Collana | Wiley-Interscience series in discrete mathematics and optimization |
| Soggetto topico |
Combinatorial analysis
Probabilities |
| ISBN |
1-280-27276-7
9786610272761 0-470-31228-9 0-471-72215-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dedication; 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 Erdős-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: Brégman's Theorem; 3 Alterations; 3.1 Ramsey Numbers; 3.2 Independent Sets; 3.3 Combinatorial Geometry; 3.4 Packing; 3.5 Recoloring
3.6 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 Rödl 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 6 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: Turán '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 8.1 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 10.8 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 13.2 Empty Triangles Determined by Points in the Plane |
| Record Nr. | UNINA-9910143188103321 |
Alon Noga
|
||
| New York : , : Interscience Publishers, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The probabilistic method / / Noga Alon, Joel H. Spencer
| The probabilistic method / / Noga Alon, Joel H. Spencer |
| Autore | Alon Noga |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | New York : , : Interscience Publishers, , [2000] |
| Descrizione fisica | 1 online resource (322 p.) |
| Disciplina | 511.6 |
| Collana | Wiley-Interscience series in discrete mathematics and optimization |
| Soggetto topico |
Combinatorial analysis
Probabilities |
| ISBN |
1-280-27276-7
9786610272761 0-470-31228-9 0-471-72215-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dedication; 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 Erdős-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: Brégman's Theorem; 3 Alterations; 3.1 Ramsey Numbers; 3.2 Independent Sets; 3.3 Combinatorial Geometry; 3.4 Packing; 3.5 Recoloring
3.6 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 Rödl 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 6 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: Turán '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 8.1 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 10.8 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 13.2 Empty Triangles Determined by Points in the Plane |
| Record Nr. | UNINA-9910830251503321 |
|
Alon Noga
|
||
| New York : , : Interscience Publishers, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||