Lecture

Probability Theory: Markov's Theorem

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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 fundamentals of probability theory, focusing on Markov's theorem and Chernoff bound. It explains the concept of good coloring, 2-colorable graphs, and hypergraphs. The instructor discusses quantitative and qualitative statements, central limit theorem, and independence of random variables. The lecture also delves into the Chernoff bound, Taylor expansion, and the existence of rare and common events.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

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