Explore the foundational principles of statistical theory and its advanced applications through random matrices. This field is crucial for understanding complex systems and high-dimensional data analysis, offering powerful tools for modeling, inference, and prediction in modern mathematical statistics.
This collection presents insightful lectures on the theory of large random matrices, focusing on their macroscopic asymptotics. Originating from the prestigious Saint-Flour Probability Summer School, these notes offer a comprehensive exploration of advanced topics in random matrix theory, crucial for researchers and students in probability and mathematical physics.
High Dimensional Probability explores the behavior of random variables and stochastic processes in spaces with a large number of dimensions. This critical field is essential for understanding and developing algorithms in modern data science, machine learning, and statistical inference, where datasets often feature numerous attributes. It delves into phenomena like concentration of measure, properties of random projections, and the geometry of high-dimensional sets, providing foundational insights for navigating complex data landscapes.