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Lecture

Martingales and Conditional Expectations

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MATH-467: Probabilistic methods in combinatorics

The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...

Description

This lecture covers the topics of Brun's Sieve, Martingales, and Conditional Expectations. It discusses the concepts of martingales with respect to random variables, the law of total expectation, and the function of support. The lecture also delves into Chernoff, Azuma, and Hoeffding inequalities, providing proofs and explanations. The instructor explores the relationship between martingales and conditional expectations, emphasizing the importance of understanding these concepts in probability theory.

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