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Lecture

Poisson Paradigm: Dependency Measures

In course

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 Poisson Paradigm, focusing on dependency measures in ordered pairs and graphs. It explains the concept of dependence and independence, as well as the constant ground set and bad sets. The instructor discusses the Chebyshev inequality, Payley-Zygmund inequality, and lower bounds. The lecture also delves into increasing and decreasing events, with examples of disjoint bad events and their implications. Various formulas and concepts related to Poisson distributions, probability, and sets are explored in detail.

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Ontological neighbourhood

Mathematics

Probability theory: Topics in probability theory

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