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In 2010, Terence Tao and Vu solved the circular law conjecture in random matrix theory, which established the non-Hermitian version of Wigner semi-circle law. In 2011, they proved the "four moment" theorem, establishing universality of local law of eigenvalues of random matrices.
This document is a worked solutions manual for the AS and A-Level Mathematics: Pure Mathematics 2 & 3 textbooks. It provides step-by-step worked solutions for problems in the textbooks on topics such as algebra, functions, coordinate geometry, calculus, and trigonometry.
In 2010, Terence Tao and Vu solved the circular law conjecture. A year later, they proved the "four moment" theorem, establishing universality of local law of eigenvalues of random matrices. Similar results were obtained around the same time by László Erdös, Horng-Tzer Yau, and Jun Yin; https://en.wikipedia.org/wiki/Terence_Tao#Random_matrices.
Random covariance matrices: universality of local statistics of eigenvalues. Zbl 1247.15036. Local resilience of graphs. Zbl 1182.05114. Additive combinatorics. Paperback reprint of the 2006 hardback ed. Zbl 1179.11002. Sparse random graphs: eigenvalues and eigenvectors. Zbl 1257.05089.
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Welcome to my webpage! I am a Persey F. Smith professor in Mathematics and a professor in Data Science at Yale University. My research foci are additive and probabilistic combinatorics, random matrices and high dimensional probability.
Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
