Lecture

Pseudorandomness: Theory and Applications

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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 concept of pseudorandomness, focusing on the theory and applications. It discusses the importance of pseudorandomness in AI, the challenges of testing properties with exponentially small probabilities, and the idea of pseudo-random graphs. The lecture also delves into the theory of dynamical systems, looking at manifolds and random walks on surfaces. It explores the transition matrix in random walks, Laplacian matrices, and the properties of adjacency matrices. Additionally, it explains the relationship between eigenvalues and eigenvectors in adjacency and Laplacian matrices, emphasizing the significance of pseudorandomness in various applications.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Algebra: Linear algebra

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