Spectral Statistics for Sparse Random Graphs

Learn about spectral statistics in sparse random graphs through a 48-minute lecture from Harvard's Theo McKenzie, exploring the fundamental properties of eigenvectors and eigenvalues in adjacency matrices and their connections to quantum physics. Delve into unique characteristics of sparse graphs, examining specific obstacles and new findings in spectral statistics. Follow along as the lecture progresses from basic spectral theory and graph algorithms to advanced concepts like the Anderson Model, infinity norm analysis, and block decomposition. Understand the relationship between sparse random graphs and quantum physics, with particular attention to concentration, eigenvalue formulas, and Poisson tail behaviors. Conclude with an exploration of limitations and engage in a Q&A session covering truncation methods and related topics.