Lecture

Gaussian Corelation Inequality & Anderson's Thum

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Description

This lecture covers the Gaussian corelation inequality, Anderson's theorem, and the Khatri-Sidak theorem. It explains the concept of convex and symmetric sets, the probability of events in these sets, and the implications of quasi-concave functions. The lecture also delves into log-concavity and its applications in probability theory, showcasing how symmetric convex sets can be represented as countable intersections. The instructor demonstrates the log-concave property and its significance in proving inequalities, providing a detailed analysis of various mathematical proofs and their implications.

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Probability

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Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

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