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The Chernoff Boundigh probability. When this is the case, we say that . is .. In this book, we will see a number of tools for proving that a random variable is concentrated, including Talagrand’s Inequality and Azuma’s Inequality. In this chapter, we begin with the simplest such tool, the Chernoff Bound.

Anticoagulant

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A First Glimpse of Total Colouring of one of them, the First Moment Method. In this chapter, we will illustrate the power of combining the other two, the Local Lemma and the Chernoff Bound, by discussing their application to total colouring.

MEET

清楚说话

Total Colouring Revisitedct with it. We then obtained a total colouring by modifying the edge colouring so as to eliminate the conflicts. In this chapter, we take the opposite approach, first choosing a vertex colouring and then choosing an edge colouring which does not conflict . with the vertex colouring, thereby obtainin

著名

Talagrand’s Inequality and Colouring Sparse Graphs close to its expected value with high probability. Such tools are extremely valuable to users of the probabilistic method as they allow us to show that with high probability, a random experiment behaves approximately as we “expect” it to.

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