| Preface | p. xi |
| Chernoff-Hoeffding Bounds | p. 1 |
| What Is "Concentration of Measure"? | p. 1 |
| The Binomial Distribution | p. 2 |
| The Chernoff Bound | p. 3 |
| Heterogeneous Variables | p. 5 |
| The Hoeffding Extension | p. 6 |
| Useful Forms of the Bound | p. 6 |
| A Variance Bound | p. 8 |
| Pointers to the Literature | p. 10 |
| Problems | p. 10 |
| Applications of the Chernoff-Hoeffding Bounds | p. 16 |
| Probabilistic Amplification | p. 16 |
| Load Balancing | p. 17 |
| Skip Lists | p. 18 |
| Quicksort | p. 22 |
| Low-Distortion Embeddings | p. 23 |
| Pointers to the Literature | p. 29 |
| Problems | p. 29 |
| Chernoff-Hoeffding Bounds in Dependent Settings | p. 34 |
| Negative Dependence | p. 34 |
| Local Dependence | p. 38 |
| Janson's Inequality | p. 39 |
| Limited Independence | p. 43 |
| Markov Dependence | p. 45 |
| Pointers to the Literature | p. 49 |
| Problems | p. 49 |
| Interlude: Probabilistic Recurrences | p. 51 |
| Problems | p. 56 |
| Martingales and the Method of Bounded Differences | p. 58 |
| Review of Conditional Probabilities and Expectations | p. 59 |
| Martingales and Azuma's Inequality | p. 61 |
| Generalising Martingales and Azuma's Inequality | p. 65 |
| The Method of Bounded Differences | p. 67 |
| Pointers to the Literature | p. 71 |
| Problems | p. 72 |
| The Simple Method of Bounded Differences in Action | p. 74 |
| Chernoff-Hoeffding Revisited | p. 74 |
| Stochastic Optimisation: Bin Packing | p. 74 |
| Balls and Bins | p. 75 |
| Distributed Edge Colouring: Take 1 | p. 76 |
| Models for the Web Graph | p. 78 |
| Game Theory and Blackwell's Approachability Theorem | p. 80 |
| Pointers to the Literature | p. 82 |
| Problems | p. 82 |
| The Method of Averaged Bounded Differences | p. 85 |
| Hypergeometric Distribution | p. 85 |
| Occupancy in Balls and Bins | p. 86 |
| Stochastic Optimisation: Travelling Salesman Problem | p. 88 |
| Coupling | p. 90 |
| Handling Rare Bad Events | p. 99 |
| Quicksort | p. 101 |
| Pointers to the Literature | p. 103 |
| Problems | p. 103 |
| The Method of Bounded Variances | p. 106 |
| A Variance Bound for Martingale Sequences | p. 107 |
| Applications | p. 110 |
| Pointers to the Literature | p. 117 |
| Problems | p. 118 |
| Interlude: The Infamous Upper Tail | p. 121 |
| Motivation: Non-Lipschitz Functions | p. 121 |
| Concentration of Multivariate Polynomials | p. 121 |
| The Deletion Method | p. 123 |
| Problems | p. 124 |
| Isoperimetric Inequalities and Concentration | p. 126 |
| Isoperimetric Inequalities | p. 126 |
| Isoperimetry and Concentration | p. 127 |
| The Hamming Cube | p. 130 |
| Martingales and Isoperimetric Inequalities | p. 131 |
| Pointers to the Literature | p. 132 |
| Problems | p. 133 |
| Talagrand's Isoperimetric Inequality | p. 136 |
| Statement of the Inequality | p. 136 |
| The Method of Non-Uniformly Bounded Differences | p. 139 |
| Certifiable Functions | p. 144 |
| Pointers to the Literature | p. 148 |
| Problems | p. 148 |
| Isoperimetric Inequalities and Concentration via Transportation Cost Inequalities | p. 151 |
| Distance between Probability Distributions | p. 151 |
| Transportation Cost Inequalities Imply Isoperimetric Inequalities and Concentration | p. 153 |
| Transportation Cost Inequality in Product Spaces with the Hamming Distance | p. 154 |
| An Extension to Non-Product Measures | p. 158 |
| Pointers to the Literature | p. 159 |
| Problems | p. 159 |
| Quadratic Transportation Cost and Talagrand's Inequality | p. 161 |
| Introduction | p. 161 |
| Review and Road Map | p. 161 |
| An L2 (Pseudo)-Metric on Distributions | p. 163 |
| Quadratic Transportation Cost | p. 165 |
| Talagrand's Inequality via Quadratic Transportation Cost | p. 167 |
| Extension to Dependent Processes | p. 168 |
| Pointers to the Literature | p. 169 |
| Problems | p. 169 |
| Log-Sobolev Inequalities and Concentration | p. 171 |
| Introduction | p. 171 |
| A Discrete Log-Sobolev Inequality on the Hamming Cube | p. 172 |
| Tensorisation | p. 174 |
| Modified Log-Sobolev Inequalities in Product Spaces | p. 175 |
| The Method of Bounded Differences Revisited | p. 177 |
| Self-Bounding Functions | p. 179 |
| Talagrand's Inequality Revisited | p. 179 |
| Pointers to the Literature | p. 181 |
| Problems | p. 181 |
| Summary of the Most Useful Bounds | p. 185 |
| Chernoff-Hoeffding Bounds | p. 185 |
| Bounds for Well-Behaved Functions | p. 185 |
| Bibliography | p. 189 |
| Index | p. 195 |
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